using slope intercept for solving systems using substitution

Solving by substitution

​Step 1; Make sure both equations are in slope intercept form

Multiple Choice

Which of these equations is in slope intercept form?

• 3x - 2y = 10

• 2x = 6y - 2

• 2y = 6x + 3

• y = 2x + 1

Multiple Choice

What is the slope intercept form for

2y = 6x + 3 ?

• It is already in slope intercept form

• y = 3x + 2/3

• y = 3x + 3/2

• y = 3x + 3

Multiple Choice

What is the slope intercept form for

2y + 4x = 6 ?

• y + 2x = 3

• y = 2x + 3

• y = 3 - 2x

• y = -2x + 3

Solving by substitution

​Step 2: since y = y, set the equations equal to each other

Example of step 2

​y = 3x + 2 y = -2x + 3

Since y = y when solving a system of equations,

3x + 2 = -2x + 3

Multiple Choice

How would you set up this system for solving for x?

y = x + 2 y = 2x + 5

• x + 2 =

  2x + 5

• x - 2 =

  2x + 5

• x + 5 =

  2x + 2

• x - 2 =

  2x - 5

Step 3: Solve for x

y = 2x + 3 y = x - 5

2x + 3 = x - 5 subtract x from both sides

x + 3 = -5 Subtract 3 from both sides

x = - 8

Multiple Choice

Solve for x

y = 6x + 4 y = 2x + 2

• x = 6/8

• x = -1/2

• x = 1/2

• x = 0

Multiple Choice

solve for x

y = 3x + 2 y = -2x - 4

• x = -6/5

• x = 6/5

• x = 5/6

• x = - 5/6

Step 4: Solve for y

y = 2x + 3 y = x - 5

2x + 3 = x - 5 subtract x from both sides

x + 3 = -5 Subtract 3 from both sides

x = - 8 Put -8 into either equation to solve for y

y = -8 - 5 y = -13

Multiple Choice

Solve for y if x = -1/2

y = 6x + 4 y = 2x + 2

• y = 1

• y = -1/2

• y = 1/2

• y = 0

Step 5: check your answer

y = 2x + 3 y = x - 5

x = - 8 y = -13

-13 = 2(-8) + 3 -13 = -8 - 5

-13 = =-16 + 3 Both answers check, the answer is (-8, -13)

Multiple Choice

Try this one on your own. Find the solution to this system:

y = x + 6 y = - x + 4

• x = 1

  y = 7

• x = 1

  y = 3

• x = - 1

  y = 5

• x = -1

  y = -5

Poll

how are you doing on this skill?