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Systems of Equations Review
By Xen McCoy
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Last updated 4 months ago
20 questions
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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
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
When there is no solution to a system of linear equations, these two lines are...
Vertical
Intersecting
Parallel
Perpendicular
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
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
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
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.
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
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
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
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
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
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)
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)
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)
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)
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
Solve for x in the system of linear equations: 3x + 2y = 12 and 6x - y = 9
4
1
2
3
Find the value of y in this system of equations: 3x + 2y = 6 and x - 4y = 8
2.857
-1.286
1
0
Given the system of equations 2x + 4y = 8 and x + y = 2, what is the solution for y?
1.5
2
1
0.5