Question

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

Explanation:

Step1: Solve for y from first equation

From \(2x + y = 3\), we can express \(y\) as \(y = 3 - 2x\).

Step2: Substitute y into second equation

Substitute \(y = 3 - 2x\) into \(4x + 4y = 8\). So we get \(4x + 4(3 - 2x)=8\).

Step3: Simplify the equation

First, expand the left - hand side: \(4x+12 - 8x = 8\). Then combine like terms: \(- 4x+12 = 8\). Subtract 12 from both sides: \(-4x=8 - 12=-4\).

Step4: Solve for x

Divide both sides of \(-4x=-4\) by \(-4\), we have \(x = \frac{-4}{-4}=1\).

Step5: Solve for y

Substitute \(x = 1\) into \(y = 3 - 2x\), then \(y=3-2\times1 = 1\).

Answer:

The solution of the system of equations is \(x = 1,y = 1\)