The first thing we need to do with this problem is to take the simpler equation and solve for one of the variables. Let's choose the second equation and solve for x.
3x-4y=1. Add 4y to each side.
3x-4y+4y=1+4y -> 3x=1+4y. Divide each side by 3.
3x/3=(1+4y)/3 -> x=(1+4y)/3. Rearange the terms inside the parenthese.
x=(4y+1)/3. Now we're ready to substitute for the x value in the first equation. We do so by replacing x, with (4y+1)/3.
7x+5y=-12 -> 7(4y+1)/3+5y=-12. Multiply the 7 in.
(28y+7)/3+5y=-12. To combine the first two terms we need a common denominator. Let's choose 3. To give 5y a denominator of 3, we multiply the top and bottom of 5y/1 by 3.
(28y+7)/3+15y/3=-12. Now combine the first terms.
(43y+7)/3=-12. Lastly we will solve for y.
(43y+7)/3*3=-12*3 -> 43y+7=-36.
43y+7-7=-36-7 -> 43y=-43.
43y/43=-43/43 -> y=-1
We have our fist varible. To solve for x, simply choose one of the original equations and plug in for y then solve for x. Let's choose the second equation once more.
3x-4y=1. Plug in value of y.
3x-4(-1)=1 -> 3x+4=1.
3x+4-4=1-4 -> 3x=-3.
3x/3=-3/3 -> x=-1
And with that, we finished solving our problem.
Hope this helped!