Question 13893
1) {{{3x+2y=12}}}
2) {{{-4x+5z=12}}}
3) {{{y-4z=-13}}} Solve this for y: {{{y = 4z-13}}} and substitute into equation 1)

1) {{{3x + 2(4z-13) = 12}}} Simplify.
{{{3x + 8z - 26 = 12}}}
1a){{{3x + 8z = 38}}} Now take equation 2)
2) {{{-4x + 5z = 12}}}  Multiply equ. 1a) by 4 and equ. 2) by 3.

1b) {{{12x + 32z = 152}}}
2a) {{{-12x + 15z = 36}}}  Now add these two to eliminate the x-term.

{{{47z = 188}}} Divide both sides by 47.
{{{z = 4}}} Substitute this into {{{y = 4z - 13}}} and solve for y.
{{{y = 4(4) - 13}}}
{{{y = 3}}} Substitute this into equation 1) and solve for x.

{{{3x + 2(3) = 12}}}
{{{3x = 6}}}
{{{x = 2}}}

x = 2
y = 3
z = 4