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
B y = -x + 4 and y = −2x + 5
Is this correct?
Yes, that is correct. The graph of the system of equations y = -x + 4 and y = -2x + 5 is a solution to the system.
Do you have proof?
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.