Question

solve the system of equations.
$-7y - 4x = 1$
$7y - 2x = 53$
$x = square$
$y = square$

Explanation:

Step1: Add the two equations

$$(-7y - 4x) + (7y - 2x) = 1 + 53$$
Simplify to eliminate $y$:
$$-6x = 54$$

Step2: Solve for $x$

$$x = \frac{54}{-6} = -9$$

Step3: Substitute $x=-9$ into second equation

$$7y - 2(-9) = 53$$
Simplify the left side:
$$7y + 18 = 53$$

Step4: Isolate and solve for $y$

Subtract 18 from both sides:
$$7y = 53 - 18 = 35$$
$$y = \frac{35}{7} = 5$$

Answer:

$x = -9$
$y = 5$