The solution to a system of two linear equations is x = 3; y = 9.
How could the intersection of the graphs of the two equations be located on a coordinate grid? Response area
What does the solution to a system of two linear equations mean on the graph? Response area
Can you have more than one solution to a Linear system of equations? Response area
Can you have exactly two solutions to a Linear system of equations? Response area
Can you have no solutions to a Linear system of equations?
Response area:
To locate the intersection of the graphs of the two linear equations on a coordinate grid, plot the point (3, 9) where the x-coordinate represents the value of x in the solution and the y-coordinate represents the value of y in the solution.
The solution to a system of two linear equations represents the point (or points) where the two graphs intersect. In other words, it is the solution of the equations when they are solved simultaneously.
It is possible to have more than one solution to a linear system of equations if the equations represent parallel lines. In this case, the lines never intersect, and there is no unique solution.
It is not possible to have exactly two solutions to a linear system of equations. A system of linear equations can have one solution, no solutions, or infinitely many solutions.
It is possible to have no solutions to a linear system of equations if the equations represent parallel lines that do not intersect. In this case, there is no point where the two lines intersect, and there is no solution to the system.
Question
x − y = −1
x−3y=−13
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?
Responses
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Unit 5 Solving Systems Review
10 of 1110 of 11 Items
Solve the system: y = −x−1
y=3x−5
Responses
(0, -1)
(-1, 1)
(1, -2)
(2, 1)
(2, 1)
− y = −1
x−3y=−13
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?
Responses
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
which one is it?
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Put the steps in order that are used to solve the following systems of equations by substitution.
{−7x −2y = −13x − 2y = 11
1. Choose one of the equations and solve for one variable in terms of the other.
2. Substitute the expression from step 1 into the other equation.
3. Solve for the remaining variable.
4. Substitute the value found in step 3 back into either equation to solve for the other variable.
5. Check the solution by substituting both values into both equations and making sure they are true.
The point (-4, 6) is a solution to which system?
Responses
{−5x+y=−2−3x+6y=−12
{−5x+y=−33x−8y=24
{−4x+y=6−5x−y=21
{x+y=2−x+2y=16