Question

solve each system of equations by elimination

1. \

$$\begin{cases} y = -x + 1 \\\\ y = 4x - 14 \\end{cases}$$

Explanation:

Step1: Rewrite equations in standard form

Rewrite \( y = -x + 1 \) as \( x + y = 1 \) and \( y = 4x - 14 \) as \( -4x + y = -14 \).

Step2: Eliminate y by subtracting equations

Subtract \( -4x + y = -14 \) from \( x + y = 1 \):
\( (x + y) - (-4x + y) = 1 - (-14) \)
\( x + y + 4x - y = 1 + 14 \)
\( 5x = 15 \)

Step3: Solve for x

Divide both sides by 5: \( x = \frac{15}{5} = 3 \)

Step4: Substitute x into one equation to find y

Substitute \( x = 3 \) into \( y = -x + 1 \): \( y = -3 + 1 = -2 \)

Answer:

The solution to the system is \( x = 3 \), \( y = -2 \) (or the ordered pair \( (3, -2) \))