Solving Systems of Equations by Elimination

Solving Systems of Equations by Elimination

By Seth Ellis

Multiple Choice

Review: What does it mean to "solve a system of equations?"

• To write equations in slope intercept form.

• To solve for x.

• To find coordinates of a point where lines cross.

• To do math stuff that is extremely hard and I'll never understand it so I'm just going to give up.

Fill in the Blanks

Review: What is the solution to this system of equations?

Q. What is an additive inverse?

​

A. Adding a number and it's opposite together always equals zero.

​

​Key Concept

Complete the Statement:

​The additive inverse of ___ is ___ because when you add them together the result is ____.

Solving Systems by Elimination

Do you see the additive inverse in this problem?

Multiple Choice

What is the additive inverse in this problem?

• -3x + 3x = 0

• Dividing -7 on both sides of the equation

• -3y + (-4y) = -7y

• (-1, -2)

Here is why "Elimination" works:

​Two ballanced scales added together still makes a ballanced scale.

Multiple Choice

If one scale had 10lbs on each side and another scale had 20lbs on each side. If i combine the weights of both scales onto a third scale, what would balanced weight be?

• Still 10lbs on each side.

• It wouldn't be balanced because math isn't a thing in real life.

• 30lbs on each side.

• You just gained some weight my dude!

Multiple Choice

Add the two equations. What is the resulting equation?

2x + 3y = 5

5x +2y = 6

• 5x + 7y = 11

• 7x + 5y = 11

• -3x + 5y = 11

• 7x + 5y = 10

Multiple Choice

When you add these two equations together, what is the resulting equation?

2y = 2x + 2

y = -2x - 5

• y = -1

• 3y = 4x + 3

• y = 0x - 3

• 3y = -3

Multiple Choice

Add: what is the resulting equation?

x - 2y = 3

-x - 4y = 9

• 0x - 6y = 12

• -2x + 6y = 12

• 6x = 12

• Don't know. :(

Finding the solution of a system of equations means finding a point. Have we found a point yet? ​

Remember!...

Multiple Choice

What should we do next to solve for the x coordinate of the point?

• Get x by itself by subtracting 3.

• Cry

• Additive Inverse

• Divide both sides by 3 to make a ghost one.

Fill in the Blanks

What is the value of x?

Multiple Choice

If x = 6, we can substitute a 6 in for x. Which x can we replace with 6?

• Only the 2x

• Only the single x

• Only the 3x

• Any x in the problem because the lines cross at a shared x value.

​2 (6) + 3y = 15

​

or

​

(6) - 3y = 3​

​It will look like this:

Now, you can solve for y.

Multiple Choice

Now try this one. What is the solution?

2y = 2x + 2

y = -2x - 5

• (-2, -5)

• (x,y)

• (-1, -2)

• (-2, -1)

This is the Elimination Method! Good work!

​Some text here about the topic of discussion.