Question

find the solution to this system: equation 1: 5x - 2y = -11 (2) equation 2: -2x + 5y = 17 (5) step 1: to create x - coefficients that are additive inverses, equation 1 can be multiplied by 2. multiplying equation 2 by 5 will create additive inverses for the x - coefficients. step 2: which is the next step to solve for y? divide by 21 on both sides of the equation. step 3: which is the next step to solve the system of equations for x?

Explanation:

Step1: Substitute y = 3 into Equation 1

Substitute \(y = 3\) into \(5x-2y=-11\), we get \(5x-2\times3=-11\).

Step2: Simplify the equation

\(5x - 6=-11\), then add 6 to both sides: \(5x=-11 + 6\), so \(5x=-5\).

Step3: Solve for x

Divide both sides of \(5x=-5\) by 5, we have \(x=\frac{-5}{5}=-1\).

Answer:

\(x=-1,y = 3\)