Answer:
X=-11
Y=8
Final: (-11,8)
Step-by-step explanation:
Isolate the Y variable
3x = -1 - 4y
3x - 1 = -4y
divide by -4
y = -3/4x - 1/4
Next equation, do the same thing
2x + 3y = 14
3y = 14 - 2x
divide by 3
y = 4 2/3 - 2/3x
Set the two equations (that are set equal to Y) equal to each other
-3/4x - 1/4 = 4 2/3 - 2/3x
+ 1/4 + 1/4
-3/4x = 11/12 - 2/3x
+2/3x +2/3x
-1/12x = 11/12
Now divide both sides by -1/12
x = -11
(11/12 was found by finding the LCM(Least Common Multiple) of 3 and 4, which is 12 and getting the equivalent factor for the denominator of 12. Same went for the -1/12)
Plug -11 in for x for one of the previous equations
3(-11) = -1 - 4y
-33 = -1 - 4y
+1 +1
-32 = -4y
Divide both sides by -4
y = 8
(-11,8)
2x - y = -2
x = 14 + 2y
Plug in the x equation
2(14+2y) - y = -2
Distribute
28 + 4y - y = -2
Combine variables
28 + 3y = -2
Subtract 28 on both sides
3y = -30
Divide the y
y = -10
