The answer is (34/11, -5/11).
First, let's rewrite the 2 equations:
[tex]3a + 5b - 7 = 0[/tex]
[tex]a - 2b - 4 = 0[/tex]
Then let's transform these 2 equations into the form ax+by=c
So that would be:
[tex]3a + 5b = 7 \\ a - 2b = 4[/tex]
Now our goal is to isolate one of the variables a or b. Lets pick a since its easier. To do this, multiply equation 2 by -3 so that 3a + -3a=0
[tex] - 3a + 6b = - 12[/tex]
Now add both equations together:
[tex] \: \: \: \: 3a + 5b = 7 \\ + - 3a + 6b = - 12 \\ \: \: \: \: 11b = - 5[/tex]
Now to isolate b, divide both sides by 11
[tex]b = - \frac{5}{11} [/tex]
Now we know the value of b, its time to solve for a
To do this, you substitute b in any equation to -5/11. In this case, I'll choose equation 2.
[tex]a - 2( - \frac{5}{11} ) = 4 \\ a + \frac{10}{11} = 4 \\ a = \frac{34}{1} [/tex]
