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
