Question

solve the system by elimination with subtraction.
$-5x + 7y = 11$
$-5x + 3y = 19$
note: enter negatives when necessary with no space between the negative sign and the number.
if the answer is fraction, do not simplify. ex. 4/3 for $\frac{4}{3}$.

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} -5x + 7y = 11 \\ -5x + 3y = 19 \end{cases}$$

Subtract the second equation from the first equation:
$$(-5x + 7y) - (-5x + 3y) = 11 - 19$$
Simplify the left side:
$$-5x + 7y + 5x - 3y = 4y$$
Simplify the right side:
$$11 - 19 = -8$$
So we get $4y = -8$.

Step2: Solve for y

Divide both sides of $4y = -8$ by 4:
$$y = \frac{-8}{4} = -2$$

Step3: Substitute y back to find x

Substitute $y = -2$ into the first equation $-5x + 7y = 11$:
$$-5x + 7(-2) = 11$$
Simplify:
$$-5x - 14 = 11$$
Add 14 to both sides:
$$-5x = 11 + 14 = 25$$
Divide both sides by -5:
$$x = \frac{25}{-5} = -5$$

Answer:

$x = -5$, $y = -2$