Question

1. \\( x + 3y = 10 \\)\\( -2x + 2y = 18 \\)

Explanation:

Step1: Solve the first equation for x

From \( x + 3y = 10 \), we can express \( x \) as \( x = 10 - 3y \).

Step2: Substitute x into the second equation

Substitute \( x = 10 - 3y \) into \( -2x + 2y = 18 \):

$$
LATEXBLOCK0
$$

Step3: Solve for y

Add 20 to both sides: \( 8y = 18 + 20 = 38 \), then \( y = \frac{38}{8} = \frac{19}{4} = 4.75 \)

Step4: Substitute y back to find x

Substitute \( y = \frac{19}{4} \) into \( x = 10 - 3y \):

$$
LATEXBLOCK1
$$

Answer:

\( x = -\frac{17}{4} \) (or -4.25), \( y = \frac{19}{4} \) (or 4.75)