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Systems of Equations Review
By Xen McCoy
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Last updated 30 days ago
20 questions
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Question 1
1.
Which method is best to use to solve the following system of linear equations? 2x + 3y = 12 and x - y = 2
Graphing method
Substitution method
Division method
Matrix method
Question 2
2.
What's the first step to solve the system using elimination? 5x + 3y = 11 and 4x - y = 9
Add the equations together
Subtract the equations
Multiply the second equation by 3
Solve one equation for y
Question 3
3.
When there is no solution to a system of linear equations, these two lines are...
Vertical
Intersecting
Parallel
Perpendicular
Question 4
4.
When you use the graphical method to solve a system of linear equations, what does the point of intersection between the two lines represent?
The x-intercept
The slope of the lines
Solution of the system
The y-intercept
Question 5
5.
When is the elimination method best used for solving a system of equations?
When coefficients of the same variable are equal
When there is only one equation
When the equations are in slope intercept form
When the equations are quadratic
Question 6
6.
In the elimination method, what happens to one of the variables when you add or subtract the equations?
It gets squared
Its value gets halved
It gets eliminated
It gets isolated
Question 7
7.
When should you use substitution to solve a system of linear equations?
When one of the equations is already solved for a variable.
When one of the variables is squared.
When the equations are not linear.
When both equations are quadratic.
Question 8
8.
In the system of equations x + 2y = 8 and 3x + 4y = 12, which variable would you solve for first using substitution?
y
x
Both x and y
Neither x nor y
Question 9
9.
Which of the following systems of equations would be best to solve using substitution?
2x + 3y = 6, 4x + 5y = 10
y = x² + 3x + 2, y = 4x - 7
y = 2x + 3, 4x - y = 1
x + y = 7, y - x = 2
Question 10
10.
When using a graph to solve a system of equations, what does the point of intersection represent?
The slope of one of the lines
The y-intercept of one of the lines
The solution to the system
A point on both lines but not solution
Question 11
11.
How many solutions does a system of linear equations have if the lines on the graph are parallel?
Infinite number of solutions
One solution
No solutions
Two solutions
Question 12
12.
How many solutions does a system of linear equations have if the lines on the graph coincide (occupy the same line)?
One solution
Two solutions
No solutions
Infinite number of solutions
Question 13
13.
Given the two equations, 2x + 3y = 6 and 4x + y = 7, which solution set satisfies these two equations?
(x, y) = (0, 2)
(x, y) = (2, 1)
(x, y) = (1, 1)
(x, y) = (1.5, 1)
Question 14
14.
Solve the system of equations: 5x + 4y = 20 and x + 2y = 3.
(x, y) = (4.667,-0.833)
(x, y) = (1, 2)
(x, y) = (2, 1)
(x, y) = (0.5, 2)
Question 15
15.
What is the solution to the system of equations: 3x - 2y = 4 and x + y = 3?
(x, y) = (1, 2)
(x, y) = (2, 1)
(x, y) = (1, 1)
(x, y) = (2, 2)
Question 16
16.
What is the solution for the system of linear equations 3x + 2y = 6 and 2x - y = 4?
(1, 2)
(2, 1)
(2, 0)
(-1, 2)
Question 17
17.
Solve the following system of linear equations: x + y = 10 and 2x - y = 4, what is the value for x?
4.667
8
5.333
2
Question 18
18.
Solve for x in the system of linear equations: 3x + 2y = 12 and 6x - y = 9
4
1
2
3
Question 19
19.
Find the value of y in this system of equations: 3x + 2y = 6 and x - 4y = 8
2.857
-1.286
1
0
Question 20
20.
Given the system of equations 2x + 4y = 8 and x + y = 2, what is the solution for y?
1.5
2
1
0.5