How do you solve 4x + y = 44x+y=4 and 2x + 8y = 02x+8y=0 using substitution?

2 Answers
Apr 9, 2016

(x,y)=(16/15,-4/15)(x,y)=(1615,415)
(see below for solution method using substitution)

Explanation:

Given: 4x+y=44x+y=4

This implies: y=4-4xy=44x
So we can substitute (4-4x)(44x) for yy
in the second given equation: 2x+8y=02x+8y=0
to get:
color(white)("XXX")2x+8(4-4x)=0XXX2x+8(44x)=0

Simplifying:
color(white)("XXX")2x+32-32x=0

color(white)("XXX")30x=32

color(white)("XXX")x=16/15

The we can substitute 16/15 for x
in the first given equation: 4x+y=4
to get:
color(white)("XXX")4*(16/15)+y=4

color(white)("XXX")y=4-64/15 = -4/15

Apr 9, 2016

(x,y)=(16/15,-4/15)

Explanation:

Solve by substitution and elimination

color(blue)(4x+y=4

color(blue)(2x+8y=0

We can eliminate 4x from the first equation by 2x in the second equation (whole equation) with -2 to get -4x

rarr-2(2x+8y=0)

Use the distributive property

color(brown)(a(b+c=x)=ab+ac=ax

rarr-4x-16y=0

Now, add the above equation with the first equation to eliminate 4x

rarr(4x+y=4)+(-4x-16y=0)

rarr-15y=4

Divide both sides by -15

rarr(cancel(-15)y)/cancel(-15)=4/-15

color(green)(rArry=-4/15

Now,substitute the value of y to the first equation

rarr4x+(-4/15)=4

rarr4x-4/15=4

Add 4/15 both sides

rarr4x-4/15+4/15=4+4/15

rarr4x=64/15

Divide both sides by 4

rarr(cancel4x)/cancel4=64/15-:4

(I have written 64/15/4 as 64/15-:4)

Take the reciprocal and multiply

rarrx=cancel64^16/15*1/cancel4^1

color(green)(rArrx=16/15

color(blue)(ul bar |(x,y)=(16/15,-4/15)|