Question

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$$\begin{aligned} y &= 7 - 3x \\\\ 4x - 3y &= 18 \\end{aligned}$$

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Explanation:

State the system of equations

We are given a system of two linear equations:

$$
LATEXBLOCK0
$$

Our goal is to find the values of \(x\) and \(y\) that satisfy both equations.

Substitute Equation 1 into Equation 2

Since Equation 1 is already solved for \(y\), we can substitute \(7 - 3x\) in place of \(y\) in Equation 2:

$$ 4x - 3(7 - 3x) = 18 $$

Distribute and simplify the equation

Distribute the \(-3\) through the parentheses:

$$ 4x - 21 + 9x = 18 $$

Combine the like terms \(4x\) and \(9x\):

$$ 13x - 21 = 18 $$

Solve for x

Add \(21\) to both sides of the equation:

$$ 13x = 39 $$

Divide both sides by \(13\):

$$ x = 3 $$

Solve for y

Substitute \(x = 3\) back into Equation 1 to find \(y\):

$$ y = 7 - 3(3) $$

$$ y = 7 - 9 $$

$$ y = -1 $$

Answer:

\(x = 3\), \(y = -1\)