Question

The graph shows the solution to which system of equations?
Responses
A y = 2x + 1 and y = 2x - 3y = 2x + 1 and y = 2x - 3
B y = -x + 4 and y = −2x + 5y = -x + 4 and y = −2x + 5
C y = 3x + 7 and y = x + 12y = 3x + 7 and y = x + 12
D y = x + 2 and y = -x - 4y = x + 2 and y = -x - 4
E y = 2x - 3 and y = −2x + 1

Answer 1

B y = -x + 4 and y = −2x + 5

Answer 2

Is this correct?

Answer 3

Yes, that is correct. The graph of the system of equations y = -x + 4 and y = -2x + 5 is a solution to the system.

Answer 4

Do you have proof?

Answer 5

Yes, the system can be solved algebraically to show that its solution is the same as the graph.

Starting with the equations:

y = -x + 4
y = -2x + 5

Set the two equations equal to each other to eliminate y:

-x + 4 = -2x + 5

Simplify and solve for x:

x = -1

Substitute x = -1 into one of the equations to solve for y:

y = -(-1) + 4

y = 5

Therefore, the solution to the system of equations is (-1, 5), which is the point where the two lines intersect. This point is also on the graph of the two equations, as shown below:


So, the graph of the system of equations y = -x + 4 and y = -2x + 5 is indeed a solution to the system.

Answer 6

Thank you!!

Answer 7

You're welcome! If you have any more questions, feel free to ask.