Question 24526
Solve:
1) {{{x+y+z = 4}}}
2) {{{x-y+2z = 8}}}
3) {{{2x+y-z = 3}}} Add equations 1) and 2) to get:
4) {{{2x+3z = 12}}} Add equations 2) and 3) to get:
5) {{{3x+z = 11}}} Multiply equation 5) by 3 to get:
6) {{{9x+3z = 33}}} Now subtract equation 4) from equation 6) to get:
7) {{{7x = 21}}} Divide both sides by 7.
{{{x = 3}}} Substitute this into equation 5) and solve for z.
{{{3(3)+z = 11}}}
{{{9+z = 11}}} Subtract 9 from both sides.
{{{z = 2}}} Finally, substitute x=3 and z=2 into equation 1) and solve for y.
{{{3+y+2 = 4}}}
{{{y+5 = 4}}} Subtract 5 from both sides.
{{{y = -1}}}

Solution:
x = 3
y = -1
z = 2

Check by substituting these values into the three equations, 1), 2), and 3)