Question

elimination with addition and subtraction
question 14 of 15 (1 point) | question attempt: 1
olve the following system of equations.
-8x + 3y = 3
13x - 3y = -18

Explanation:

Step1: Add the two equations

To eliminate \( y \), we add the two given equations: \((-8x + 3y)+(13x - 3y)=3+(-18)\). The \( 3y \) and \( -3y \) cancel out. So we have \(-8x + 13x=3 - 18\), which simplifies to \(5x=-15\).

Step2: Solve for \( x \)

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

Step3: Substitute \( x \) to find \( y \)

Substitute \( x = - 3\) into the first equation \(-8x+3y = 3\). We get \(-8\times(-3)+3y=3\), which is \(24 + 3y=3\). Subtract \(24\) from both sides: \(3y=3 - 24=-21\). Then divide by \(3\): \(y=\frac{-21}{3}=-7\).

Answer:

\(x=-3\), \(y = - 7\)