Question

solve using substitution.

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$$\begin{aligned} 2x - y &= 18 \\\\ 2x + y &= 6 \\end{aligned}$$

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\\((\quad, \quad)\\)

Explanation:

🆕 New Concept Discovered: Solving Systems of Equations by Substitution
Replace one variable with an equivalent expression from another equation.

Step 1: Isolate a variable

We can isolate \( y \) in the second equation:

$$ 2x + y = 6 $$

$$ y = 6 - 2x $$

Step 2: Substitute into the other equation

Substitute \( y = 6 - 2x \) into the first equation:

$$ 2x - (6 - 2x) = 18 $$

$$ 2x - 6 + 2x = 18 $$

$$ 4x - 6 = 18 $$

$$ 4x = 24 $$

$$ x = 6 $$

Step 3: Solve for the remaining variable

Substitute \( x = 6 \) back into the expression for \( y \):

$$ y = 6 - 2(6) $$

$$ y = 6 - 12 $$

$$ y = -6 $$

Answer:

(6, -6)