6.3: Solving Systems by Substitution

2x - 3y = -1

y = x - 1

What is the correct first step if you are solving this system by substitution?

• Substitute (x - 1) for the "y" in the top equation.

• Isolate the x in the bottom equation.

• Substitute the (x - 1) for the "x" in the top equation.

• You shouldn't be using substitution. This is set up for elimination.

Answer explanation

The correct first step is to substitute (x - 1) for 'y' in the top equation, 2x - 3y = -1. This allows us to express the system in terms of one variable, making it easier to solve.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

-3x - 3y = 3

y = -5x - 17

Dana wants to solve the system using Substitution. Which is the correct first step?

Answer explanation

To solve the system using substitution, substitute the expression for y from the second equation into the first equation. This leads to -3x - 3(-5x - 17) = 3, which is the correct first step.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

y = -3x + 5

5x - 4y = -3

Billy is solving this system by substitution. Which is the correct first step of his work?

Answer explanation

Billy should substitute the expression for y from the first equation into the second equation. Thus, the correct first step is 5x - 4(-3x + 5) = -3, which simplifies the system using substitution.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (4, 40)

• (-4, 40)

• (40, 4)

• (-40, 4)

Answer explanation

Substituting y=10x into x+y=44 gives x+10x=44, or 11x=44. Solving for x, we find x=4. Substituting back, y=10(4)=40. Thus, the solution is (4, 40).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (1, 7)

• (7, 1)

• (-1, -7)

• (-7, -1)

Answer explanation

Substituting y=7x into x+y=8 gives x+7x=8, or 8x=8. Thus, x=1. Substituting x=1 back into y=7x gives y=7. The solution is (1, 7), which matches the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (-3, -6)

• (-3, 6)

• (3. 3)

• (-3, 3)

Answer explanation

Substituting y=3 into -4x-4y=-24 gives -4x-12=-24. Solving for x, we find x=3. Thus, the solution is (3, 3), which matches the correct answer.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• No solution

• (-6, 0)

• (2, 0)

• (3, 0)

Answer explanation

Substituting y=2x-4 into 2x-8y=4 gives 2x-8(2x-4)=4. Simplifying leads to 2x-16x+32=4, or -14x= -28, resulting in x=2. Plugging x back gives y=0. Thus, the solution is (2, 0).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (-1, -4)

• (1, -4)

• (1, 4)

• (-3, -4)

Answer explanation

Substituting y from the second equation into the first gives 2x + 4(-4x + 8) = 18. Simplifying leads to 2x - 16x + 32 = 18, or -14x = -14, so x = 1. Substituting x back gives y = 4. Thus, the solution is (1, 4).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• Student A

• Student B

• Neither student is correct

Answer explanation

To verify, substitute (7, -5) into both equations: 2(7) + 6(-5) = -16 and -5 = -3(7) + 16. Both hold true. For (-7, -5), only the second equation holds. Thus, Student A is correct.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• 8

• -3

• 0

• -6

Answer explanation

To find the X-value, substitute y from the second equation into the first: -6x - 2(5x - 8) = 16. Simplifying gives -6x - 10x + 16 = 16, leading to -16x = 0. Thus, x = 0.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6