Question

solving systems of linear equations: substitution
what is the solution to the system of equations?
y = \frac{1}{3}x - 10
2x + y = 4
(6, -8)
(16, -6)
(-6, 16)
(-8, 6)

Explanation:

Step1: Substitute \( y \) into the second equation

We know \( y = \frac{1}{3}x - 10 \), substitute it into \( 2x + y = 4 \):
\( 2x + (\frac{1}{3}x - 10) = 4 \)

Step2: Simplify and solve for \( x \)

Combine like terms: \( 2x+\frac{1}{3}x - 10 = 4 \)
\( \frac{6x + x}{3}-10 = 4 \)
\( \frac{7x}{3}-10 = 4 \)
Add 10 to both sides: \( \frac{7x}{3}=4 + 10 \)
\( \frac{7x}{3}=14 \)
Multiply both sides by 3: \( 7x = 14\times3 \)
\( 7x = 42 \)
Divide by 7: \( x=\frac{42}{7}=6 \)

Step3: Find \( y \) using \( x = 6 \)

Substitute \( x = 6 \) into \( y=\frac{1}{3}x - 10 \):
\( y=\frac{1}{3}\times6 - 10 \)
\( y = 2 - 10=-8 \)

Answer:

\((6, -8)\)