Solving System of Equations Substitution Method

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

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

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

x - y = 0

18x + 2y = 0

Step 4:

In step 2, we got x = 0 and y = 0, what is the final answer?

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Which statement is correct to begin to solve this equation?

• The variable is already isolated in the first equation, so we have already solved it.

• The variable is already isolated in the first equation, so we have to plug into the second one like this:

  -4(4-2x) - 2y = -8

• The variable is already isolated in the first equation, so we have to plug into the second one like this:

  -4x - 2(4 - 2x) = -8

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Example 3: y = 4 - 2x -4x - 2y = -8 Finish step 2 (which shows correct steps): -4x - 2(4 - 2x) = -8

• -4x - 2(4 - 2x) = -8

  -4x - 8 + 4x = -8

  8 = -8

• -4x - 2(4 - 2x) = -8

  -4x - 8 - 4x = -8

  -8x - 8 = -8

  -8x = 0

  x = 0

• -4x - 2(4 - 2x) = -8

  -4x - 8 + 4x = -8

  -8 = -8

• -4x - 2(4 - 2x) = -8

  -4x - 8 - 2x = -8

  -6x - 8 = -8

  -6x = 0

  x = 0

Tags

CCSS.8.EE.C.7B

y = 4 - 2x

-4x - 2y = -8

In step 2, we got -8 = -8.

What does this mean?

• The answer is

  (-8, -8).

• Infinitely Many Solutions

• No Solution

• We made a mistake.

Tags

CCSS.8.EE.C.8B

• Infinitely Many Solutions
• No Solution

Tags

CCSS.8.EE.C.8A

Which is the best method for solving this system of equations?

• Substitution

• Elimination

• Equal Values

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6