Solving System of Equations by Substitution Method

The first step in solving using the substitution method is __________.

• get x by itself
• get y by itself
• get either variable by itself
• add the equations together

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

When solving a system of equations algebraically, which statement results in infinite solutions?

• 4 = 7

• 2 = 2

• -3 = 3

• all of the above

Tags

CCSS.8.EE.C.8B

When solving a system of equations algebraically, which statement results in no solution?

• 4 = 7

• -2 = 2

• -3 = 3

• all of the above

Tags

CCSS.8.EE.C.8B

Example 1

Steps 1 and 2a:

Step 1: Solving for a variable.

Step 2a: Substitute

y = 6x

2x + 5y = 32

This step is what EOC likes to test on!

• The variable is already isolated, so we've already solved the system.

• The variable is already isolated for y, so we substitute it in the second equation like this:

  2(6x) + 5y = 32

• The variable is already isolated for y, so we substitute it in the second equation like this:

  2x + 5(6x) = 32

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Example 1

Step 2 part b: Solve answer from step 2 part a.

Solve 2x + 5(6x) = 32

• x = 0

• x = 1

• x = -1

• x = 4

Tags

CCSS.8.EE.C.7B

Example 1

Step 3:

After substituting the first equation into the second one and working it out, I got

x = 1.

What should I do next? Then do it.

• Fill in 1 for x in y = 6x

  y = 6(1)

  y = 6

• Fill in 1 for y in y = 6x

  1 = 6x

  1/6 = x

• Fill in 1 for y in 2x + 5y = 32

  2x + 5(1) = 32

  2x + 5 = 32

  2x = 27

  x = 27/2

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Example 1

Step 4:

What is the solution to the system:

y = 6x

2x + 5y = 32

Given I got x = 1 from step 2 and y = 6 from step 3.

• (1, 6)

• (6, 1)

Tags

CCSS.HSA.REI.C.7

Example 2:

x - y = 0

18x + 2y = 0

Which statement would be correct for step 1 and do it?

• I would solve the first equations for y because it has a coefficient of 1.

  y = -x

• I would solve the first equations for y because it has a coefficient of -1.

  -y = -x

• I would solve the first equations for x because it has a coefficient of 1.

  x = y

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Example 2:

x - y = 0

18x + 2y = 0

Step 2:

In step 1, we got x = y.

Which shows the correct steps for step 2 (substituting and solving)?

• 18x + 2y = 0

  18(y) + 2y = 0

  20y = 0

  No Solution

• 18x + 2y = 0

  18(y) + 2y = 0

  20y = 0

  y = 0

Tags

CCSS.8.EE.C.8B

Example 2:

x - y = 0

18x + 2y = 0

Step 3:

In step 2, we got y = 0.

What do I next? Do it.

• I will plug y = 0 into the equation x = y.

  x = y

  x = (0)

  x = 0

• I will plug y = 0 into the equation x = y.

  x = y

  (0) = y

  0 = y

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6