Question 120624
Solve the first equation for y:
{{{y=-2x+9}}}
Substitute this y into the second equation:
{{{-3x+2(-2x+9)=4}}}
{{{-7x=-14}}} Combine terms on the left, subtract 19 from both sides
{{{x=2}}} Divide both sides by -7.

Now, substitute this value of x into the first equation where we solved for y in terms of x: {{{y=-2(2)+9=-4+9=5}}}.

This gives the solution set S:{2,5}.


Additionally, we could solve this system through techniques of linear algebra as follows: 
Matrix: 
|2  1  9|
|-3 2  4|

(3/2)R1+R2->
|2  1       9|
|0  7/2  35/2|

(1/2)R1->
|1  1/2   9/2|
|0  7/2  35/2|

(2/7)R2->
|1  1/2   9/2|
|0  1      5 |

-1/2R2+R1->
|1  0      2 |
|0  1      5 |

Making S={2,5} the only solution.