Question

solve the system of linear equations by substitution. enter your answer as an ordered pair. \\(\

$$\begin{cases} x - 3y = -20 \\\\ 3x - 4y = -10 \\end{cases}$$

\\)

Explanation:

Step1: Solve first equation for x

From \( x - 3y = -20 \), we get \( x = 3y - 20 \).

Step2: Substitute x into second equation

Substitute \( x = 3y - 20 \) into \( 3x - 4y = -10 \):
\( 3(3y - 20) - 4y = -10 \)
Expand: \( 9y - 60 - 4y = -10 \)
Simplify: \( 5y - 60 = -10 \)
Add 60 to both sides: \( 5y = 50 \)
Divide by 5: \( y = 10 \)

Step3: Substitute y back to find x

Substitute \( y = 10 \) into \( x = 3y - 20 \):
\( x = 3(10) - 20 = 30 - 20 = 10 \)

Answer:

\((10, 10)\)