M8 Lesson 15 Day 2 Substitution

What is the first step in solving a system by Substitution?

• Make sure both equations are in standard form.

• Make sure at least one equation is solved for one variable.

• Make sure both equations are in slope-intercept form.

• Make sure both equations can be solved.

Which answer has a correct first step for this system:

3x + 3y = 3

y = 3x + 5

• 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 first equation and solve for x

  3x + 3(3x + 5) = 3

• Take a nap

• The variable is already isolated for y, so we substitute it in the second equation and solve for x

  y = 3(3x + 3y) = 3

Continue with the next step of solving the system from question 2.

3x + 3y = 3

y = 3x + 5

STEP 1: 3x + 3(3x + 5) = 3

• 3x + 9x +15 = 3

• 3x + 6x + 15 = 3

• 3x + 9x + 5 = 3

• 6x(3x+5)=3

Answer explanation

You must distribute first by doing 3 times 3x and 3 times 5.

Continue with the next step of solving the system from question 3.

3x + 3y = 3

y = 3x + 5

STEP 1: 3x + 3(3x + 5) = 3

STEP 2: 3x + 9x +15 = 3

• 9x +15 = -3x + 3

• 3x + 24 = 3

• 6x + 15 = 3

• 12x + 15 = 3

Answer explanation

Combine Like Terms 3x and 9x

Continue with the next step of solving the system from question 4.

3x + 3y = 3

y = 3x + 5

STEP 1: 3x + 3(3x + 5) = 3

STEP 2: 3x + 9x +15 = 3

STEP 3: 12x + 15 = 3

Solve for x

• x = 1

• x = -1

• x = 6

• x = -6

Answer explanation

Subtract 15 from both sides.

Divide by 12

Continue with the next step of solving the system from question 5.

3x + 3y = 3

y = 3x + 5

STEP 1: 3x + 3(3x + 5) = 3

STEP 2: 3x + 9x +15 = 3

STEP 3: 12x + 15 = 3

STEP 4: x = -1

Solve for y using y=3x+5

• y = -2

• y = 3

• y = 2

• y = 5

Answer explanation

Substitute X= -1 into y=3x+5.

3(-1)+5

-3+5

2

Continue with the next step of solving the system from question 6.

3x + 3y = 3

y = 3x + 5

STEP 1: 3x + 3(3x + 5) = 3

STEP 2: 3x + 9x +15 = 3

STEP 3: 12x + 15 = 3

STEP 4: x = -1

STEP 5: y = 2

What is the solution of the system?

• ( 2,-1)

• (-1,2)

Answer explanation

Solutions are written as (x,y)

What is the solution to the following system:

(Hint: Use your Day 1 Notes For Help)

^{y = 5x}

^{3x + y = 24}

• ^{(15, 3)}

• ^{(3, 5)}

• ^{(3, 15)}

• ^{(5, 3)}

What is the solution to the following system?

^{y = 3x}

^{12x - 4y = 20}

• (0, 0)

• no solutions

• (0, 20)

• infinite solutions

What is the solution to the following system?

^{x = -2y}

^{3x + 4y = -8}

• (-2, -8)

• (4, 3)

• (-2, 4)

• (-8, 4)