Identify the solution to the system of linear equations.

Question

y = -3x + 2

y = x - 6

Responses

(2, -4)
(2, -4)

(4, -2)
(4, -2)

(1, -1)
(1, -1)

(0, 2)

Answer 1

To find the solution to the system of linear equations given by:

1. $y=-3x+2$
2. $y=x-6$

We can set the two equations equal to each other since both expressions represent $y$:

$$-3x+2=x-6$$

Now, let's solve for $x$:

1. Add $3x$ to both sides:

$$2=4x-6$$

2. Add $6$ to both sides:

$$8=4x$$

3. Divide both sides by $4$:

$$x=2$$

Now that we have $x$, we can substitute it back into either of the original equations to find $y$. We'll use the second equation:

$$y=2-6$$ $$y=-4$$

Thus, the solution to the system of equations is $(2,-4)$.

Checking with the first equation:

$$y=-3(2)+2=-6+2=-4$$

Both equations give $y=-4$ when $x=2$, confirming the solution.

The answer is $\boxed{{\displaystyle (2,-4)}}$.