Question

1. what is the solution to the following system of equations?

$y = \frac{1}{3}x - 2$
$4y + 3x = 18$
(□,□)

Explanation:

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

We know \( y = \frac{1}{3}x - 2 \), substitute this into \( 4y + 3x = 18 \).
So we get \( 4(\frac{1}{3}x - 2) + 3x = 18 \).

Step2: Simplify the equation

First, expand the left - hand side:
\( 4\times\frac{1}{3}x-4\times2 + 3x=18\)
\(\frac{4}{3}x-8 + 3x=18\)
Combine like terms: \(\frac{4}{3}x+3x=18 + 8\)
Convert \(3x\) to thirds: \(3x=\frac{9}{3}x\), so \(\frac{4}{3}x+\frac{9}{3}x=\frac{13}{3}x\)? Wait, no, wait. Wait, \(4\times\frac{1}{3}x=\frac{4}{3}x\), and \(3x=\frac{9}{3}x\), so \(\frac{4}{3}x+\frac{9}{3}x=\frac{13}{3}x\)? Wait, no, that's a mistake. Wait, let's do it again.
Wait, \(4(\frac{1}{3}x - 2)+3x=18\)
\(4\times\frac{1}{3}x-8 + 3x=18\)
\(\frac{4}{3}x+3x=18 + 8\)
\(3x=\frac{9}{3}x\), so \(\frac{4}{3}x+\frac{9}{3}x=\frac{13}{3}x\)? Wait, no, 4/3 x+3x = (4/3 + 9/3)x=13/3 x? Wait, but 18 + 8 = 26. So \(\frac{13}{3}x=26\)
Then solve for x: \(x = 26\times\frac{3}{13}\)
\(26\div13 = 2\), so \(x=2\times3 = 6\)

Step3: Find the value of y

Substitute \(x = 6\) into \(y=\frac{1}{3}x-2\)
\(y=\frac{1}{3}\times6-2\)
\(y = 2-2=0\)

Answer:

\((6,0)\)