Question

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

y = -1/2x + 6
y = 3x - 1

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 see if the equations hold true.

For the equation y = -1/2x + 6:

Substituting x = 5 and y = -3:

-3 = -1/2(5) + 6
-3 = -5/2 + 6
-3 = -5/2 + 12/2
-3 = 7/2

Since -3 is not equal to 7/2, (5, -3) is not a solution to the equation y = -1/2x + 6.

Now, let's check if the point (5, -3) is a solution to the equation y = 3x - 1:

Substituting x = 5 and y = -3:

-3 = 3(5) - 1
-3 = 15 - 1
-3 = 14

Since -3 is not equal to 14, (5, -3) is not a solution to the equation y = 3x - 1.

Therefore, the point (5, -3) is not a solution to the system of equations.