Solving Systems with Substitution

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

• get x by itself

• get y by itself

• get either variable by itself in one equation

• add the equations together

Tags

CCSS.HSA.REI.C.6

What does
"solution to a system of equations"
mean?

• It's the point where both equations equal zero
• It's the point where graphs of both equations cross the y-axis
• It's the point that solves both equations at the same time
• It's the point where graphs of both equations cross the x-axis

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.D.11

CCSS.HSA.REI.D.10

• Substitute y with x-1 to get 2x -3(x - 1) = -1

• Substitute y with x-1 to get 2(x - 1) -3y = -1

Tags

CCSS.HSA.REI.A.1

Which variable can we substitute?

x = -3y - 17

2x + 3y = -7

• Substitute x with -3y -17 to get 2(-3y - 17) + 3y= -7

• Substitute x with -3y -17 to get 2x + 3(-3y - 17) = -7

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.CED.A.2

Which equation is correctly using substitution for the system shown?

x = -3y - 8

x - 2y = -3

• -3y -8 -2y = -3

• x(-3y -8) -2y = -3

• x -2(-3y-8) = -3

Tags

CCSS.HSA.REI.C.6

How would you correctly substitute for this system?

y = 5x + 1

y = 3x + 13

Student answer y= 5(3x +13) +1

• Replace the y in the second equation with 5x +1 and get 5x +1 = 3x +13

• Replace the y in the first equation with 3x+ 13 and get 3x +13 = 5x +1

• Replace the y in the first equation with 3x+ 13 and get y = 5(3x+13) +1

• Replace the y in the second equation with 5x +1 and get y = 3(5x +1) +13

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.A.1

Which answer has a correct first step for this system:

3x + 3y = 3

y = 3x + 5

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

• The variable is already isolated for y, so we substitute it in the first equation 3(3x + 5) + 3y = 3 and then solve for x

• The variable is already isolated for y, so we substitute it in the first equation 3x + 3(3x + 5) = 3 and then solve for x

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.A.1

Which answer has a correct first step for this system:

-3x +y = -14

x = -2y + 14

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

• The variable is already isolated for x, so we substitute it in the first equation -3x - 2y +14 = -14 and then solve for y

• The variable is already isolated for x, so we substitute it in the first equation -3(14 - 2y) +y = -1 and then solve for y

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.REI.A.1

Which equation is correctly using substitution for the system shown? (Select more than 1 answer.)

^{x = 4y +7}

^{x = 4y}

• 4y = 4y +7

• 4y +7 = 4y

• x = 4(4y +7)

• x = 4(4y) +7

Tags

CCSS.HSA.REI.C.6

Which equation is correctly using substitution for the system shown? (Select more than 1 answer.)

y = x + 6

y = -2x − 3

• x + 6 = -2x − 3

• y = − 2x − 3 + 6

• -2x − 3 = x + 6

• y = − 2(x+6) − 3

Tags

CCSS.HSA.REI.C.6