Steps Systems of Equations by Substitution

Now that we know x = 3

(from the previous question).

Solve the system.

**Write your answer as an ordered pair**

(a)  

Answer explanation

We know x = 3, so plug it into one of the equation to solve for y.

y = 3x - 5

y =3(3)-5

y = 9 - 5

y = 4

So our answer is (3,4).

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Which of the following correctly shows substituting the first equation into the second equation?

• x + 3x = -32

• y + y = -32

• y = 3(x + y = -32)

• 3y + y = -32

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Which of the following correctly shows substituting the first equation into the second equation?

• y = 9(2x + 10) - 2

• 9x - 2 = 3x + 10

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Solve the system.

**Use the correct answer from the previous question to help you**

• (2, 16)

• (4, 2)

• (1, 13)

• (1, -3)

Answer explanation

9x - 2 = 3x + 10

6x = 12

x = 2

Plug back in to find y.

y = 9x - 2

y = 9(2) -2

y = 18 - 2

y = 16

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Which of the following correctly shows substituting the first equation into the second equation?

• 5x = -x + 4

• 5(y + 4) + 6y = 13

• 5x + 6(-x + 4) = 13

• 5x + (-x + 4) = 13

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Which of the following correctly shows substituting the second equation into the first equation?

Answer explanation

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Solve the system.

**Use the correct answer from the previous question to help you**

• (-7, 0)

• (-3, -19)

• (1, 2)

• (-3, 1)

Answer explanation

-8(-7 + 4y) - 5y = 19

56 - 32y - 5y = 19

56 -37y = 19

-37y = -37

y = 1

Plug y back in to find x.

x = -7 + 4y

x = -7 + 4(1)

x = -7 + 4

x = -3

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Which of answer shows the correct steps to solve for x?

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

When you solve a system by substitution you get a different solution then when you solve the same system by graphing.

• True

• False

• Sometimes

Answer explanation

The solution to a system means the same no matter which of the 3 methods we use for solving.

The solution is the point(s) on the line that both lines share no matter which solving method we use!

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3

Solve the system.

**Use the correct answer from the previous question to help you**

• (-14, 11)

• (11, 15)

• (11, 11)

• (11, -7)

Answer explanation

5x + 6(-x + 4) = 13

5x - 6x + 24 = 13

-1x + 24 = 13

-1x = -11

x = 11

Plug in x to find y.

y = -x + 4

y = -(11) + 4

y = -11 + 4

y = -7

Tags

CCSS.MATH.CONTENT.HSA.REI.C.6

CCSS.MATH.CONTENT.HSA.CED.A.3