Answer:
1) Solution (2,-3)
2) Solution (-1, [tex]-\frac{3}{2}[/tex])
3) Solution ([tex]\mathbf{-\frac{1}{2},-\frac{5}{2}}[/tex])
Step-by-step explanation:
We need to solve equations using elimination
1) [tex]2x+2y=-2\\3x-2y=12[/tex]
Let:
[tex]2x+2y=-2--eq(1)\\3x-2y=12--eq(2)[/tex]
Adding both equations:
[tex]2x+2y=-2\\3x-2y=12\\--------\\5x=10\\x=\frac{10}{5}\\x=2[/tex]
We get value of x = 2
Now, put value of x into equation 1 to find value of y
[tex]2x+2y=-2\\Put\:x=2\\2(2)+2y=-2\\4+2y=-2\\2y=-2-4\\2y=-6\\y=-6/2\\y=-3[/tex]
So, we get y = -3
Solution (2,-3)
2) [tex]4x-2y=-1\\-4x+4y=-2[/tex]
Let:
[tex]4x-2y=-1--eq(1)\\-4x+4y=-2--eq(2)[/tex]
Adding both equations
[tex]4x-2y=-1\\-4x+4y=-2\\------\\2y=-3\\y=\frac{-3}{2}[/tex]
We get: y= -3/2
Now find value of x by putting value of y in eq(1)
[tex]4x-2y=-1\\Put\:y=\frac{-3}{2}\\4x-2( \frac{-3}{2})=-1\\4x+3=-1\\4x=-1-3\\4x=-4\\x=\frac{-4}{4}\\x=-1[/tex]
We get x = -1
Solution (-1, [tex]-\frac{3}{2}[/tex])
3) [tex]x-y=2\\x+y=-3[/tex]
let:
[tex]x-y=2--eq(1)\\x+y=-3--eq(2)[/tex]
Add both equations:
[tex]x-y=2\\x+y=-3\\-----\\2x=-1\\x=-\frac{1}{2}[/tex]
We get x = -1/2
Now, put value of x in equation 2
[tex]x+y=-3\\-\frac{1}{2}+y=-3\\y=-3+ \frac{1}{2}\\y=\frac{-6+1}{2}\\y=\frac{-5}{2}[/tex]
We get y = -5/2
Solution ([tex]\mathbf{-\frac{1}{2},-\frac{5}{2}}[/tex])
