How do you solve 0x – 8y = -16 and -8x + 2y = 36 ?

2 Answers
Jan 20, 2018

x = -4
y = 2

Explanation:

We can use the elimination method to solve this system.

Equation 1: 0x - 8y = -16
Equation 2: -8x + 2y = 36

In the elimination method, we multiply each equation by a suitable number so that the two equations have a like term. For this problem, we will be focusing on y.

First, we will multiply equation 1 by the coefficient of y in equation 2, and multiply equation 2 by the coefficient of y in equation 1.

This means will will be multiplying equation 1 by color(red)2 and multiplying equation 2 by color(blue)(-8).

Equation 1: color(red)2 \times (0x color(blue)( - 8)y = -16)
Equation 2: color(blue)(-8) \times (-8x + color(red)2y = 36)

New Equation 1: 0x - 16y = -32
New Equation 2: 64x -16y = -288

Now that both equations have a like term (-16y), we can subtract the second equation from the first equation to eliminate them.

=> (0x - 16y = -32) - (64x -16y = -288)

=> -64x +0y = 256

=> -64x = 256

Now all we have to do is divide both sides by -64 to isolate and solve for x:

(-64x)/-64 = (256)/-64

color(magenta)(x = -4)

We can then substitute x into either equation 1 or equation 2 to solve for y. I will be using equation 2.

Substitute x with -4:
64(-4) -16y = -288

-256 -16y = -288

Add 256 to both sides:
-256 color(red)(+ 256) -16y = -288color(red)(+ 256)
-16y = -32

Divide both sides by -16 to isolate y.
(-16y)/-16 = (-32)/-16

color(magenta)(y = 2)

- - Alternate method: - -

As you may have noticed, equation 1 has a term 0x. color(red)(0x) will equate to color(red)0 no matter the value of x, so the equation can be converted into:

-8y = -16

We can then divide both sides by -8 to solve for y:

(-8y)/-8 = (-16)/-8

color(magenta)(y = 2)

Then substitute the value of y in to the second equation and solve for x:

-8x + 2(2) = 36

-8x + 4 = 36

Subtract 4 from both sides of the equation:

-8x + 4 color(red)(-4)= 36 color(red)(-4)

-8x = 32

Then divide both sides by -8 to solve for x:

(-8x)/-8 = (32)/-8

color(magenta)(x = -4)

The point (-4,2) is the point of intersection between the two lines.

graph{(-8y+16)(2y-8x-36)=0 [-12.66, 12.65, -6.33, 6.33]}

Feb 6, 2018

0x simply means 0... so you can add as many variables as you want if there's a 0 behind them...

So... in the first equation
=>0x-8y=-16
=>0-8y=-16
=>-8y=-16
Cancel out the minuses
=>8y=16
=>y=16/8
=>color(red)(y=2
Put this value in the second equation

Second equation
-8x+2y=36
Put value
-8x+2xx2=36
Multiply
-8x+4=36
Transfer the value 4
-8x=32
Transfer -8
x=32/(-8)
color(red)(x=-4