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