Question

use substitution to solve the system of equations.
2x + y = 3
4x + 4y = 8

Explanation:

Step1: Solve for y in first equation

From \(2x + y = 3\), we get \(y = 3 - 2x\).

Step2: Substitute y into second equation

Substitute \(y = 3 - 2x\) into \(4x + 4y = 8\):
\(4x + 4(3 - 2x) = 8\)
Expand: \(4x + 12 - 8x = 8\)
Simplify: \(-4x + 12 = 8\)
Subtract 12: \(-4x = -4\)
Divide: \(x = 1\).

Step3: Find y using x=1

Substitute \(x = 1\) into \(y = 3 - 2x\):
\(y = 3 - 2(1) = 1\).

Answer:

\((1, 1)\)