Can this cancel out

Question

Y=-x-2

Y=3x+2

can -x cancel out 3x

Answer 1

You have two equations, both equal to Y, so if Y=Y, then -x - 2 = 3x + 2. you can solve for x.

-4x = 4 x = -1

Now you can substitute x = -1 into either equation to get the equivalent y value. (It's -1)

Answer 2

Gotcha! Let's do this using elimination and substitution. Elimination: So we have to artificially multiply 3 with

y = -x-2 to cancel out our x. This will give you -3x-6

Now we have the following:

-3x-6

3x+2

---------- (add)

We get: y = -4

Plug in Y= -4 into any of the equations to solve for x.

Ex: -4 = 3x+2

X = -2

Thus one possible solution to this system of equations is: (-2, -4)

We can check if this solution is TRUE or not by simply plugging our points back into the equations.

Y=-x-2

Y=3x+2

-4 = - (-2) -2

-4 = 0 This is FALSE. Thus, we cannot solve this system of equations by elimination.

Lets try using substitution: 3x+2 = -x-2

4x = -4

x = -1

Let's find y: I'll plug the x value into any given equation.

y = 3(-1) +2

y = -3 +2 = -1

or

y = - ( - 1 ) - 2

See, we get the same y value regardless of where we plug in the x value.

y = -1

Let's verify if our solution is TRUE.

(-1,-1)

y = 3x+2

-1 = 3(-1) +2

-1 = -1 TRUE

y = -x-2

- 1 = - ( - 1 ) - 2

-1 = -1 TRUE

ANS: For that reason, substitution works, and our solution is (-1,-1) You can also verify this graphically using DESMOS online calculator or a graphing calculator. You will notice that (-1,-1) is the point of intersection of both equations. I hope this helps! :)