Question

What is the solution to 3x -2y =1 and 4y = 7 + 3x

Answer 1

Given.

$3x-2y=1$ (1)

$4y=7+3x$ (2)

Re-arrange equation (2)

$(4y=7+3x)-4y$

$0=-4y+3x+7$

$(0=-4y+3x+7)-7$

$-7=-4y+3x$

Multiply equation (2) by -1

$-1(3x-4y=-7)$

$-3x+4y=7$(3)

Combine like terms and solve.

$3x-3x-2y+4y=1+7$

$2y=8$

Divide by (2y) and solve for (y).

$\frac{2y}{2}=\frac{8}{2}$

$y=4$

Substitute (y) for equation (1).

$3x-2y=1$

$3x-2(4)=1$

$3x-8=1$

Add (8) to both sides.

$(3x-8)+8=(1)+8$

$3x=9$

Divide by (3).

$\frac{3x}{3}=\frac{9}{3}$

$x=3$

Check your work.

$3x-2y=1$

$3(3)-2(4)=1$

$9-8=1$

$1=1$

$4y=7+3x$

$4(4)=7+3(3)$

$16=7+9$

$16=16$

Your answers is $x=3$ and $y=4$