2x- 3y= -2 and 3x-2y= 12 by elimination method
Answers
Answer:2x−3y=−23x−2y=12
Consider the first equation. Multiply −2 and 3 to get −6.
2x−3y=−6x−2y
Add 6x to both sides.
2x−3y+6x=−2y
Combine 2x and 6x to get 8x.
8x−3y=−2y
Add 2y to both sides.
8x−3y+2y=0
Combine −3y and 2y to get −y.
8x−y=0
Consider the second equation. Multiply −2 and 3 to get −6.
−6x−2y=12
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
8x−y=0,−6x−2y=12
To make 8x and −6x equal, multiply all terms on each side of the first equation by −6 and all terms on each side of the second by 8.
−6×8x−6(−1)y=0,8(−6)x+8(−2)y=8×12
Simplify.
−48x+6y=0,−48x−16y=96
Subtract −48x−16y=96 from −48x+6y=0 by subtracting like terms on each side of the equal sign.
−48x+48x+6y+16y=−96
Add −48x to 48x. Terms −48x and 48x cancel out, leaving an equation with only one variable that can be solved.
6y+16y=−96
Add 6y to 16y.
22y=−96
Divide both sides by 22.
y=−
11
48
Substitute −
11
48
for y in −6x−2y=12. Because the resulting equation contains only one variable, you can solve for x directly.
−6x−2(−
11
48
)=12
Multiply −2 times −
11
48
.
−6x+
11
96
=12
Subtract
11
96
from both sides of the equation.
−6x=
11
36
Divide both sides by −6.
x=−
11
6
The system is now solved.
x=−
11
6
,y=−
11
48
Step-by-step explanation:
Solve for x, y
x=−
11
6
≈−0.545454545
y=−
11
48
=−4
11
4
≈−4.363636364
elimination method