Question 75152
Solve the system of equations:
1) {{{3x+2y = 12}}}
2) {{{2x+5y = 8}}}
Your suggestion is a good one.
1a) {{{-2(3x+2y) = -2(12)}}}
1a) {{{-6x-4y = -24}}}
2a) {{{3(2x+5y) = 3(8)}}}
2a) {{{6x+15y = 24}}}
Now add equations 1a) and 2a)
1a) {{{-6x-4y = -24}}}
2a) {{{6x+15y = 24}}}
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3) {{{11y = 0}}} so y = 0 Now substitute this value for y into either of the two original equations and solve for x.
1) {{{3x+2y = 12}}} Set y = 0
{{{3x+2(0) = 12}}}
{{{3x = 12}}} Divide both sides by 3.
{{{x = 4}}}
The solution is: (4, 0)
Here's the graph showing the intersection (solution).
{{{graph(300,200,-5,7,-5,5,-(3/2)x+6,-(2/5)x+8/5)}}}