Question 324946
Solve by eliminiation:
{{{2y+3x = 12}}}
{{{-4y+5x = -2}}}
Here you have two equations in two unknowns.  The idea behind the "elimination" method is to eliminate one of the variables (either x or y) then solve for the remaining variable.  Once you know the value of one of the variables, you can find the value of the other one by substitution.
Let's start:
1) {{{2y+3x = 12}}} Multiply this equation by 2.
2) {{{-4y+5x = -2}}}
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1a) {{{4y+6x = 24}}}
2a) {{{-4y+5x = -2}}} Add these two equations to eliminate the y-variable.
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3) {{{11x = 22}}} Divide both sides by 11.
3a) {{{highlight(x = 2)}}} Now substitute this value of x into either one of the two original equations to solve for y. Let's use equation 1).
1) {{{2y+3x = 12}}} Substitute x = 2.
1a) {{{2y+3(2) = 12}}}
1b) {{{2y+6 = 12}}} Subtract 6 from both sides.
1c) {{{2y = 6}}} Divide both sides by 2.
1d) {{{highlight(y = 3)}}}