Is (1,–1) a solution to this system of equations?

Question

y=–6x+5
y=x–2
yes or no

Answer 1

To determine if the point (1, –1) is a solution to the system of equations given by:

1. \( y = -6x + 5 \)
2. \( y = x - 2 \)

We will substitute \( x = 1 \) and \( y = -1 \) into both equations.

For the first equation:

Substituting \( x = 1 \):

\[ y = -6(1) + 5 = -6 + 5 = -1 \]

The left-hand side equals the right-hand side, so \( (1, -1) \) satisfies the first equation.

For the second equation:

Substituting \( x = 1 \):

\[ y = 1 - 2 = -1 \]

The left-hand side again equals the right-hand side, so \( (1, -1) \) also satisfies the second equation.

Since the point (1, –1) satisfies both equations, the answer is yes.