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
