Question

ve the following system of equations. -3x + y = 17 7x + y = -23

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases}-3x + y = 17 \\ 7x + y = -23\end{cases}$$

Subtract the first equation from the second equation:
$$(7x + y) - (-3x + y) = -23 - 17$$
Simplify the left side: $7x + y + 3x - y = 10x$
Simplify the right side: $-40$
So we get $10x = -40$

Step2: Solve for x

Divide both sides of $10x = -40$ by 10:
$$x = \frac{-40}{10} = -4$$

Step3: Substitute x into one equation to find y

Substitute $x = -4$ into the first equation $-3x + y = 17$:
$$-3(-4) + y = 17$$
Simplify: $12 + y = 17$
Subtract 12 from both sides: $y = 17 - 12 = 5$

Answer:

$x = -4$, $y = 5$