Question

find the solution to this system: equation 1: 5x - 2y = -11 (2) equation 2: -2x + 5y = 17 step 1: to create x - coefficients that are additive inverses, equation 1 can be multiplied by 2. multiplying equation 2 by will create additive inverses for the x - coefficients 2 5 10

Explanation:

Step1: Analyze the x - coefficients

Equation 1 is \(5x - 2y=-11\), and Equation 2 is \(-2x + 5y = 17\). We want to make the x - coefficients additive inverses. If we multiply Equation 1 by 2, the x - coefficient becomes \(2\times5 = 10\). To make the x - coefficient of Equation 2 the additive inverse of 10, we need to multiply Equation 2 by 5 since \(-2\times5=-10\).

Step2: Multiply the equations

Multiply Equation 1: \(2(5x - 2y)=2\times(-11)\), which gives \(10x-4y=-22\). Multiply Equation 2: \(5(-2x + 5y)=5\times17\), which gives \(-10x + 25y=85\).

Answer:

5