Question

solve each system.

1. $5x = -2 - 2y$

$1 - \frac{1}{6}x - \frac{1}{3}y = 0$

Explanation:

Step1: Simplify the second equation

Multiply the second equation \(1 - \frac{1}{6}x - \frac{1}{3}y = 0\) by 6 to eliminate fractions:
\(6\times1 - 6\times\frac{1}{6}x - 6\times\frac{1}{3}y = 6\times0\)
\(6 - x - 2y = 0\)
Rearrange to get: \(x + 2y = 6\) → \(x = 6 - 2y\)

Step2: Substitute \(x = 6 - 2y\) into the first equation

First equation: \(5x = -2 - 2y\)
Substitute \(x\): \(5(6 - 2y) = -2 - 2y\)
Expand: \(30 - 10y = -2 - 2y\)

Step3: Solve for \(y\)

Add \(10y\) to both sides: \(30 = -2 + 8y\)
Add 2 to both sides: \(32 = 8y\)
Divide by 8: \(y = 4\)

Step4: Solve for \(x\)

Substitute \(y = 4\) into \(x = 6 - 2y\):
\(x = 6 - 2(4) = 6 - 8 = -2\)

Answer:

\(x = -2\), \(y = 4\)