Question

solve the system by substitution. -6x + 8y = -18 3x = y

Explanation:

Step1: Substitute \( y = 3x \) into the first equation

We know from the second equation that \( y = 3x \). Substitute this into \( -6x + 8y = -18 \), so we get \( -6x + 8(3x) = -18 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side of the equation: \( -6x+24x=-18 \), which combines to \( 18x = - 18 \). Divide both sides by 18: \( x=\frac{-18}{18}=-1 \).

Step3: Find the value of \( y \)

Since \( y = 3x \) and \( x=-1 \), substitute \( x = - 1 \) into \( y = 3x \), we get \( y=3\times(-1)=-3 \).

Answer:

The solution to the system is \( x = - 1 \) and \( y=-3 \), or the ordered pair \( (-1,-3) \).