Question

use substitution to solve the system.
-2x + y = 14
3x - 2y = -23
x =

y =

Explanation:

Step1: Solve for y from first equation

From \(-2x + y = 14\), we can express \(y\) in terms of \(x\) by adding \(2x\) to both sides. So, \(y = 2x + 14\).

Step2: Substitute y into second equation

Substitute \(y = 2x + 14\) into the second equation \(3x - 2y = -23\). We get \(3x - 2(2x + 14) = -23\).

Step3: Simplify and solve for x

First, expand the equation: \(3x - 4x - 28 = -23\). Combine like terms: \(-x - 28 = -23\). Add 28 to both sides: \(-x = 5\). Multiply both sides by -1: \(x = -5\).

Step4: Substitute x to find y

Substitute \(x = -5\) into \(y = 2x + 14\). So, \(y = 2(-5) + 14 = -10 + 14 = 4\).

Answer:

\(x = -5\)
\(y = 4\)