Question

What is the value of the x variable in the solution to the following system of equations? 4x − 3y = 3 5x − 4y = 3

Answer 1

Solve 4x − 3y = 3 and  5x − 4y = 3

Step 1: Solve for x in 4x-3y=3:
4x-3y=3
4x-3y+3y=3+3y [Add 3y to both sides]
4x=3y+3
$\frac{4x}{4} = \frac{3x+3}{4}$ [Divide both sides by 4]
x=$\frac{3}{4}y+ \frac{3}{4}$

Step 2: Substitute $\frac{3}{4}y+ \frac{3}{4}$ for x in 5x-4y=3
5x-4y=3
5($\frac{3}{4}y+ \frac{3}{4}$)-4y=3
$\frac{-1}{4}y+ \frac{15}{4} =3$
$\frac{-1}{4}y+ \frac{15}{4} - \frac{15}{4} =3- \frac{15}{4}$ [Subtract $\frac{15}{4}$ to both sides]
$\frac{-1}{4}y= \frac{-3}{4}$
$\frac{ \frac{-1}{4}y}{ \frac{-1}{4} }= \frac{\frac{-3}{4} }{ \frac{-1}{4}}$ [Divide both sides by $\frac{-1}{4}$ ]
y = 3

Step 3: Substitute 3 for y in x = $\frac{3}{4}y+ \frac{3}{4}$
$\frac{3}{4}y+ \frac{3}{4}$
$\frac{3}{4}(3)+ \frac{3}{4}$
x = 3