Question

use substitution to solve the system.
-2x + 3y = -5
-3x + y = -11
x =

y =

Explanation:

Step1: Solve for y from the second equation

From \(-3x + y = -11\), we can express \(y\) in terms of \(x\) by adding \(3x\) to both sides. So, \(y = 3x - 11\).

Step2: Substitute y into the first equation

Substitute \(y = 3x - 11\) into \(-2x + 3y = -5\). We get \(-2x + 3(3x - 11) = -5\).

Step3: Simplify and solve for x

First, expand the equation: \(-2x + 9x - 33 = -5\). Combine like terms: \(7x - 33 = -5\). Add 33 to both sides: \(7x = -5 + 33 = 28\). Then divide both sides by 7: \(x = \frac{28}{7} = 4\).

Step4: Substitute x back to find y

Substitute \(x = 4\) into \(y = 3x - 11\). So, \(y = 3(4) - 11 = 12 - 11 = 1\).

Answer:

\(x = 4\)
\(y = 1\)