Question

Is the point (5, -3) a solution to this system of equations?

y = x - 8
2x + y = 7

Answer 1

To determine if the point (5, -3) is a solution to the system of equations, we can substitute the values of x and y into each equation and check if the equations hold true.

For equation 1:
y = x - 8
-3 = 5 - 8
-3 = -3
The equation holds true.

For equation 2:
2x + y = 7
2(5) + (-3) = 7
10 - 3 = 7
7 = 7
The equation holds true.

Since both equations hold true when the values of x = 5 and y = -3, the point (5, -3) is indeed a solution to the system of equations.