Systems of Equations with Steps

Put the steps for solving by SUBSTITUTION in order:

• Plug that number into the other equation

• Solve for the second variable

• Plug the resulting expression into the other equation

• Solve one equation for x or y

• Solve for the first variable

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=​9-3y.

Fill in the blanks to plug that expression in and solve for y:

4(​9-3y)-2​y =-6

36-​12y-2y=​-6

36-​14y =-6

-14y=​ (a)  

y=​ (b)  

• -42

• 3

• 30

• -3

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Put the steps for solving by ELIMINATION in order:

• Solve for the remaining variable

• Plug that number into either original equation and solve for the other variable

• Make sure the equations are lined up

• Subtract the equations to eliminate one variable

• Multiply one or both equations by a number to get common but opposite coefficients

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Let's solve a system by GRAPHING. Put the steps in order from first to last.

• The intersection point is the solution

• Graph both lines using the slope and y-intercept

• Solve both equations for y to get slope-intercept form

Tags

CCSS.8.EE.C.8B

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Tags

CCSS.HSA.CED.A.3

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Tags

CCSS.8.EE.C.8C

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

Tags

CCSS.HSA.CED.A.3

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=​

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

In this system

x+3y=9

4x-2y=-6

it'll be easiest to start by solving the first equation for x.

The result of doing so is x=​9-3y.

Fill in the blanks to plug that expression in and solve for y:

4(​ (a)   )-2​ (b)   =-6

36-​ (c)   y-2y=​ (d)  

36-​ (e)   =-6

• 9-3y

• y

• 12

• -6

• 14y

• x

• 10y

• x+3y

• 24y

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6