Question 12503
Solve by elimination:

1) {{{x + 2z = 5}}}
2) {{{-4x + 6y = 0}}}
3) {{{x - 2z = 9}}}

Add equations 1) and 3) to eliminate z.

{{{x + 2z = 5}}}
{{{x - 2z = 9}}}
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{{{2x = 14}}}
{{{x = 7}}}  Substitute this value of x into equation 1) and solve for z.

1)
{{{7 + 2z = 5}}} Subtract 7 from both sides.
{{{2z = -2}}} Divide both sides by 2.
{{{z = -1}}} 
Substitute x = 7 into equation 2) and solve for y.

{{{-4(7) + 6y = 0}}}
{{{-28 + 6y = 0}}} Add 28 to both sides.
{{{6y = 28}}} Divide both sides by 6.
{{{y = 28/6}}} = 4 2/3

To check the solutions, substitute x = 7, y = 4 2/3, and z = -1 into the original equations.  I'll leave for you to do.