Question

solve the system by the substitution method.
5x - y = -12
x + 4y = 6

Explanation:

Step1: Solve for one variable

From the first equation \(5x - y = -12\), solve for \(y\).
Add \(y\) to both sides: \(5x + 12 = y\), so \(y = 5x + 12\).

Step2: Substitute into second equation

Substitute \(y = 5x + 12\) into the second equation \(x + 4y = 6\).
We get \(x + 4(5x + 12) = 6\).

Step3: Simplify and solve for x

Expand the equation: \(x + 20x + 48 = 6\).
Combine like terms: \(21x + 48 = 6\).
Subtract 48 from both sides: \(21x = 6 - 48 = -42\).
Divide both sides by 21: \(x = \frac{-42}{21} = -2\).

Step4: Solve for y

Substitute \(x = -2\) into \(y = 5x + 12\).
\(y = 5(-2) + 12 = -10 + 12 = 2\).

Answer:

The solution to the system is \(x = -2\), \(y = 2\) (or as an ordered pair \((-2, 2)\))