Systems of Equations - Recap

What is the first step?

y = x + 8

x + y = 2

• substitute x + 8 for y in the second equation

• substitute x + 8 for x in the second equation

• substitute x + y for y in the first equation

What is first step?

x = 3y

2x + 4y = 10

• 2x + 4(3y) = 10

• 2(3y) + 4y = 10

• x = 3(2x + 4y)

What is the next step?

y = -2x - 2

5x + 3y = -8

Step 1: 5x + 3(-2x - 2) = 8

Step 2: ?

• Distribute the 3

• Subtract the 5x

• Add 8 to both sides

• Add 5x to both sides

What is the next step?

5x + 2y = 7

y = -4x + 8

Step 1: 5x + 2(-4x + 8) = 7

Step 2: 5x - 8x + 16 = 7

Step 3: -3x + 16 = 7

Step 4:

• add 3x to each side

• subtract 7 from each side

• subtract 16 from each side

• add 16 to each side

What is the next step?

2x - 3y = -12

y = -x + 9

Step 1: 2x - 3(-x + 9) = -12

Step 2: 2x + 3x - 27 = -12

Step 3: 5x - 27 = -12

Step 4: 5x = 15

Step 5: x = 3

Step 6: ?

• substitute 3 for x in y = -x + 9

• substitute 3 for x in 2x - 3y = -12

• either option will work

What is the first step?

2x - 3y = 14

x + 3y = -11

• solve each equation for y

• add the equations to eliminate the y's

• subtract the equations to eliminate the y's

What is the next step?

-3x - 4y = -1

3x - y = -4

Step 1: -5y = -5

Step 2: ?

• add 5 to both sides

• subtract 5 from both sides

• multiply -5 to both sides

• divide both sides by -5

What is the next step?

-2x - y = 12

9x + y = -26

Step 1: 7x = -14

Step 2: x = -2

Step 3: ?

• substitute -2 in for x in either equation

• substitute -2 in for y in either equation

• Nothing. The problem is solved.

What's the next step?

-2x + 4y = -8

5x - 4y = 20

Step 1: 3x = 12

Step 2: x = 4

Step 3: 5(4) - 4y = 20

Step 4: 20 - 4y = 20

• divide both sides by -4

• add 20 to both sides

• subtract 20 from both sides

• add 4 to both sides

Challenge question:

If you needed to create opposites in this problem, what could you do?

3x - 4y = -14

3x + 2y = -2

• multiply either equation by -1

  (to create opposites and eliminate the x's)

• multiply the bottom equation by 2

  (to create opposites and eliminate the y's)

• subtract the equations (top-bottom)

  (to eliminate the x's)

• all options would work