Review Substitution Method

Review Substitution Method

STEPS FOR USING SUBSTITUTION METHOD

• ​Make sure AT LEAST ONE EQUATION is in the form of y = ......​

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• ​Substitute one equation into the other!

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• ​Solve for x!

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• ​Substitute your x value into an original equation to find your y value!

Multiple Choice

y = 5x

y = 2x + 3

Are either equation in the system above in the form of y =...?

• Neither say y =..

• Only the top equation says y =...

• Only the bottom equation says = ...

• Both equations are in the form of y =...

Multiple Choice

y = 5x

y = 2x + 3

We will substitute top equation into the bottom, what does the substitution look like?

• y = y

• y = 5x

• 5x = 2x + 3

• y = 2x + 3

Multiple Choice

After substituting we end up with:

5x = 2x + 3

How do we start solving for x?

• Variables are both sides, so let's move them together!

• Move the +3 to the other side!

• Wait for Mr. G to solve it...

Multiple Choice

After substituting we end up with:

5x = 2x + 3

Let's move variables! But how do we do it?

• Move the bigger one, 5x, to the right side.

• Move the + 3 to the left side

• Move the smaller one, 2x, to the left side.

Multiple Choice

After substituting we end up with:

5x = 2x + 3

When we move 2x, do we flip the sign or keep it the same?

• Flip the sign, make it -2x!

• Keep it as 2x!

Multiple Choice

After moving 2x, we end up:

5x - 2x = 3

3x = 3

Solve for x

• x = 3

• x = 1

• x = -3

• x = -1

Multiple Choice

We know x = 1 and our original system is:

y = 5x

y = 2x + 3

Substitute x = 1 into either equation to solve for y.

• y = 1

• y = 5

• y = 2

• y = 3

Multiple Choice

Try solving this system on your own now:

y = 2x -2

y =3x

• x = -2

  y = -6

  (-2,-6)

• x = 6

  y =2

  (6,2)

• x = 1

  y = 6

  (1,6)

• x = 0

  y = -2

  (0,-2)

Multiple Choice

Lets try a new type of problem

y = 3x + 8

8x + 4y = 12

Are either equation in the system above in the form of y =...?

• Neither say y =..

• Only the top equation says y =...

• Only the bottom equation says = ...

• Both equations are in the form of y =...

Multiple Choice

Lets sub the top equation into the bottom one.

y = 3x + 8

8x + 4y = 12

What is the end result?

• 8x + 4y = 12

• 8x + 4y = 3x + 8

• 8x + 4(3x + 8) = 12

Multiple Choice

8x + 4(3x + 8) = 12

Lets deal with the 4(3x + 8)

After we distribute what do we end up with?

• 3

• 4x + 8

• 12x + 32

Multiple Choice

We end up with this!

8x + 12x + 32= 12

When we collect like terms what do we end up with?

• 12x + 32 = 12

• 20x + 32 = 12

• 8x + 32 = 12

Multiple Choice

We end up with this!

20x + 32 = 12

Solve this two step equation.

• x = 20

• x = -1

• x = 5

Multiple Choice

We end up with x = -1

Sub it into the original equations to find y value

y = 3x + 8

8x + 4y = 12

• y = 20

• y = 5

• y = 1

Multiple Choice

Try solving this system on your own now:

y = 2x + 1

3x + 4y = 26

• (0,6)

• (2,5)

• (3,5)