Given.
[tex]3x-2y=1[/tex] (1)
[tex]4y=7+3x[/tex] (2)
Re-arrange equation (2)
[tex](4y=7+3x)-4y[/tex]
[tex]0=-4y+3x+7[/tex]
[tex](0=-4y+3x+7)-7[/tex]
[tex]-7=-4y+3x[/tex]
Multiply equation (2) by -1
[tex]-1(3x-4y=-7)[/tex]
[tex]-3x+4y=7[/tex](3)
Combine like terms and solve.
[tex]3x-3x-2y+4y=1+7[/tex]
[tex]2y=8[/tex]
Divide by (2y) and solve for (y).
[tex]\frac{2y}{2}=\frac{8}{2}[/tex]
[tex]y=4[/tex]
Substitute (y) for equation (1).
[tex]3x-2y=1[/tex]
[tex]3x-2(4)=1[/tex]
[tex]3x-8=1[/tex]
Add (8) to both sides.
[tex](3x-8)+8=(1)+8[/tex]
[tex]3x=9[/tex]
Divide by (3).
[tex]\frac{3x}{3}=\frac{9}{3}[/tex]
[tex]x=3[/tex]
Check your work.
[tex]3x-2y=1[/tex]
[tex]3(3)-2(4)=1[/tex]
[tex]9-8=1[/tex]
[tex]1=1[/tex]
[tex]4y=7+3x[/tex]
[tex]4(4)=7+3(3)[/tex]
[tex]16=7+9[/tex]
[tex]16=16[/tex]
Your answers is [tex]x=3[/tex] and [tex]y=4[/tex]
