3x+4y=9
4x-37=-13
OK, you did write the equations down incorrectly. They should be:
3x+4y = 9
4x-3y = -13
Let's re-write them in standard form y = mx+b
3x+4y = 9
4y = 9 - 3x
y = (9/4) - (3/4)x
4x-3y=-13
-3y = -13 - 4x
y = (13/3) + (4/3)x
Now set the two equations equal. This is the point where the two lines intersect:
(9/4) - (3/4)x = (13/3) + (4/3)x
(9/4) - (13/3) = (4/3)x + (3/4)x
-25/12 = (25/12)x
-1 = x
Solve for y by plugging x = -1 into either original equation:
3x + 4y = 9
3(-1) + 4y = 9
-3 + 4y = 9
4y = 12
y = 3
Answer is (-1,3)
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