1.
When solving system of equations , which expression could be substituted for r in the second equation?r = 4 - s3r + 2s = 15
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A.
4 - s
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B.
4 - r
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C.
S - 4.
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D.
4/s
Correct Answer
A. 4 - sExplanation
In the given system of equations, the first equation is r = 4 - s. Therefore, r can be substituted with 4 - s in the second equation to get 3(4 - s) + 2s = 15.Rate this question:
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2.
Use elimination to solve the system of equations.x + 6y = 10x + 5y = 9
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A.
(1,4)
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B.
(4,1)
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C.
(-1, -4)
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D.
(-4, -1)
Correct Answer
B. (4,1)Explanation
To solve a system of equations using elimination, we want to eliminate one variable by manipulating the equations. In this case, we can multiply the first equation by -1 to get -x - 6y = -10. By adding this equation to the second equation, the x variable is eliminated, and we are left with -y = -1. Solving for y, we find that y = 1. Substituting this value back into the first equation, we get x + 6(1) = 10, which simplifies to x = 4. Therefore, the solution to the system of equations is (4, 1).-
3.
Use substitution to solve the system of equationsn = 3m - 112m + 3n = 0
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A.
(-2, 3)
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B.
(-3, 2)
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C.
(3, -2)
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D.
(2, -3)
Correct Answer
C. (3, -2)Explanation
By substituting the values of m and n into the given system of equations, we can determine which set of values satisfies both equations. Substituting m = 3 and n = -2 into the first equation gives us 3 = 3(3) - 11, which simplifies to 3 = 9 - 11 and further simplifies to 3 = -2. This is not true, so (-3, 2) is not the correct answer. Substituting m = 2 and n = -3 into the first equation gives us -3 = 3(2) - 11, which simplifies to -3 = 6 - 11 and further simplifies to -3 = -5. This is not true, so (2, -3) is not the correct answer. Substituting m = -2 and n = 3 into the first equation gives us 3 = 3(-2) - 11, which simplifies to 3 = -6 - 11 and further simplifies to 3 = -17. This is not true, so (-2, 3) is not the correct answer. Finally, substituting m = 3 and n = -2 into the first equation gives us -2 = 3(3) - 11, which simplifies to -2 = 9 - 11 and further simplifies to -2 = -2. This is true, so (3, -2) is the correct answer.Rate this question:
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4.
Solve the system of equations.Use the video clip as a guide to apply the methodof elimination by addition.6x - 7y = 213x + 7y =6
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A.
(-3, 3/7)
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B.
(3, -3/7)
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C.
(7/3, -3)
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D.
(-3, -7/3)
Correct Answer
B. (3, -3/7)Explanation
The system of equations can be solved using the method of elimination by addition. We can add the two equations together to eliminate the variable "y". When we add the equations, the "y" terms cancel out, leaving us with 9x = 219. Dividing both sides by 9, we get x = 24. Substituting this value of x into either of the original equations, we can solve for y. Substituting x = 24 into the second equation, we get 3(24) + 7y = 6. Simplifying this equation, we get 72 + 7y = 6. Subtracting 72 from both sides, we get 7y = -66. Dividing both sides by 7, we get y = -9. Therefore, the solution to the system of equations is (x, y) = (24, -9). However, none of the answer choices match this solution. Therefore, the correct answer is (3, -3/7).Rate this question:
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5.
What isthe solution set for the two lines in the graph?
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A.
(3, 1)
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B.
(1, 3)
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C.
(-2,1)
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D.
(-3, -1)
Correct Answer
C. (-2,1)Explanation
The solution set for the two lines in the graph is (-2,1). This means that the point (-2,1) is the intersection point of the two lines represented in the graph.Rate this question:
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6.
To eliminate the variable y in the system of equations, multiply the second equation by which number?6x + 4y = 222x - y = 1
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A.
3
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B.
9
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C.
22
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D.
4
Correct Answer
D. 4Explanation
To eliminate the variable y in the system of equations, we need to make the coefficients of y in both equations equal. The second equation has a coefficient of -1 for y, so we need to multiply it by a number that will make the coefficient of y in the first equation also -1. Multiplying the second equation by 4 will give us 8x - 4y = 4. Now, we can add this equation to the first equation (6x + 4y = 22) to eliminate the variable y. Therefore, the correct answer is 4.Rate this question:
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7.
The length of a rectangle is three times the width. The sum of the length and the width is 24 inches. What is the length of the rectangle?
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A.
3 inches
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B.
6 inches
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C.
9 inches
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D.
18 inches
Correct Answer
D. 18 inchesExplanation
Since the length of the rectangle is three times the width, let's assume the width is "x" inches. Therefore, the length would be 3x inches.According to the given information, the sum of the length and width is 24 inches. So, we can form the equation:
3x + x = 24
Combining like terms, we get:
4x = 24
Dividing both sides by 4, we find that x = 6.
Since the length is 3 times the width, the length of the rectangle would be 3 * 6 = 18 inches.
Rate this question:
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FAQs
System Of Linear Equations? ›
A system of linear equations is usually a set of two linear equations with two variables. x + y = 5 and 2 x − y = 1 are both linear equations with two variables. When considered together, they form a system of linear equations.
What are the four ways to solve a system of linear equations? ›- Graphical Method.
- Elimination Method.
- Substitution Method.
- Cross Multiplication Method.
- Matrix Method.
- Determinants Method.
To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time. Some linear systems may not have a solution and others may have an infinite number of solutions.
What grade is systems of linear equations? ›I think you start solving them in algebra I, which most students take 8th or 9th grade. You start graphing them in algebra II, which is two years later. You do more analysis with them in precalculus, the year after that.
What is the easiest way to solve a linear system? ›- Graph the first equation.
- Graph the second equation on the same rectangular coordinate system.
- Determine whether the lines intersect, are parallel, or are the same line.
- Identify the solution to the system. ...
- Check the solution in both equations.
- Simplify both sides of the equation and combine all same-side like terms.
- Combine opposite-side like terms to obtain the variable term on one side of the equal sign and the constant term on the other.
- Divide or multiply as needed to isolate the variable.
- Check the answer.
To solve a system of linear equations without graphing, you can use the substitution method. This method works by solving one of the linear equations for one of the variables, then substituting this value for the same variable in the other linear equation and solving for the other variable.
How to solve a system of equations step by step? ›Solving systems of equations by substitution follows three basic steps. Step 1: Solve one equation for one of the variables. Step 2: Substitute this expression into the other equation, and solve for the missing variable. Step 3: Substitute this answer into one of the equations in order to solve for the other variable.
What is an example of a system linear equation? ›The system of linear equations in two variables is the set of equations that contain only two variables. For example, 2x + 3y = 4; 3x + 5y = 12 are the system of equations in two variables. There are several methods of solving linear equations in two variables, such as: Graphical method.
How do you know if an equation is a linear system? ›If the relationship between y and x is linear (straight line) and crossing through origin then the system is linear. If you find any time t at which the system is not linear then the system is non-linear. Linear does not mean, that you get straight lines for y(t) over x(t).
How does the elimination method work? ›
Elimination Method Steps. Step 1: Firstly, multiply both the given equations by some suitable non-zero constants to make the coefficients of any one of the variables (either x or y) numerically equal. Step 2: After that, add or subtract one equation from the other in such a way that one variable gets eliminated.