Solving Systems using Substitution

Question

-6x-8y=2

6x-8y=14

Answer 1

To solve this with substitution you need to convert both equations to slope-intercept form

-6x-8y=2->-8y=2+6x->y=-2/8+-6/8x

6x-8y=14->6x-8(-2/8+-6/8x)=14

6x+2+6x=14->12x+2=14->12x=12->x=12/12->x=1

6(1)-8y=14->6-8y=14->-8y=8->y=8/-8 or y=-1

6(1)-8(-1)=14->6+8=14

-6(1)-8(-1)=2->-6+8=2

x=1, y=-1 this is the solution.

Answer 2

To solve a system of equations using substitution, we need to use one of the equations to solve for one of the unknown variables. Then, we will plug that solution into the solved variable in the other equation.

We can do this in any order, with any equation, and with any variable. For the sake of this walkthrough, we'll use the first equation to solve for the variable x.

-6x - 8y = 2

To get the x term alone, I'll add 8y to both sides.

-6x = 2 + 8y

Now, I'll divide both sides by -6 so I have x alone.

x = (2 + 8y) / -6

Now that we have a definition for x, we can use it to plug in as x in the second equation. This moves us closer to the answer because it makes the only variable in the second equation y. To begin, I'll replace the x in the second equation with the definition I found for x from the first equation.

6((2 + 8y) / -6) - 8y = 14

I'll start simplifying so I can solve for y. I first notice that the 6 and -6 at the beginning of the problem will cancel to -1, which I will distribute throughout the (2 + 8y) term.

-2 - 8y - 8y = 14

Now, I'll combine the like terms (the y terms).

-2 - 16y = 14

To get the y term alone, I'll add 2 to both sides.

-16y = 16

Finally, I'll divide both sides of the equation by -16 to solve for y.

y = -1

Now that we have the value of y, we can plug that into either equation and solve for x. I like that the x term is already positive in the second equation, so I'll use that one.

6x - 8(-1) = 14

6x + 8 = 14

We'll subtract 8 from both sides.

6x = 6

Finally, we will divide both sides by 6 to get x alone.

x = 1

It's always a good idea to plug your answers back in and make sure they produce the answer you expect.

-6(1) - 8(-1)

-6 + 8

2, which is the answer we expected for the first equation.

6(1) - 8(-1)

6 + 8

14, which is the answer we expected for the second equation.

I hope this helped!

Answer 3

Adding the equations gives -16y = 16, so y = -1

Substituting y =-1 into second

6x -8 (-1) = 14

6x + 8 = 14

6x = 6

x = 1