How do solve the following linear system?: x+2y=1 , -2x -8y = 4 x+2y=1,2x8y=4?

2 Answers
Feb 1, 2017

x=4x=4 and y=-3/2y=32 or -1 1/2112

Explanation:

x+2y=1x+2y=1
-2x-8y=42x8y=4

Reduce the second equation by dividing all terms by 22.

-2x-8y=42x8y=4

-x-4y=2x4y=2

Multiply all terms by -11.

x+4y=-2x+4y=2

Separate 4y4y into two.

x+2y+2y=-2x+2y+2y=2

In this equation, substitute (x+2y)(x+2y) with color(red)(1)1, the value from the first equation.

x+2y+2y=-2x+2y+2y=2

color(red)(1)+2y=-21+2y=2

Subtract 11 from both sides.

2y=-32y=3

Divide both sides by 22.

y=-3/2=-1 1/2y=32=112

In the first equation, substitute yy with color(blue)(-3/2)32.

x+2y=1x+2y=1

x+2color(blue)((-3/2))=1x+2(32)=1

Open the brackets and simplify.

x-3=1x3=1

Add 33 to both sides.

x=4x=4

Feb 1, 2017

y=-1 1/2, x=4y=112,x=4

Explanation:

x+2y=1x+2y=1-----------(1)

-2x-8y=42x8y=4---------(2)

2x+4y=22x+4y=2 (1) xx 2 (1)×2 ---------(3)

-4y=64y=6--------(2)+(3)

4y=-64y=6

y=-6/4y=64

y=-1 1/2y=112

Substitute y=-6/4y=64 in ----------1

x+2(-6/4)=1x+2(64)=1

x-12/4=1x124=1

x-3=1x3=1

x=1+3x=1+3

x=4x=4
Substitute #y= -6/4,x=4 in------1

4+2(-6/4)=14+2(64)=1

4-12/4=14124=1

multiply both sides by 4
16-12=41612=4

4=44=4