Wednesday, September 11 th Please complete the warm up

Wednesday, September 11th

Please complete the warm up

1. What is the slope and y intercept?

-2x + 5y = 152. Describe each graph

X= 5 y= -6

Ticket to Go Answers

Homework Answers

Y = 2x – 1 and y = -3x + 3

What went

wrong?

Y = 2x – 1 and y = -3x + 3

Where is the

solution?

What do we do!?!?!?

Since we can’t just “estimate” this specific point, we will use something called:

SUBSTITUTION

SubstitutionGood News….You already know how

to do this!Substitution is when you replace a

known value for an equivalent quantity.

Examples of substitution in real life:A recipe calls for ground beef and

you substitute ground turkeyWhen Jay Cutler is a being a baby,

they have to substitute in a different player

SOLVING SYSTEMS

OF EQUATIONS BY

SUBSTITUTION

•Remember Steps in math our like recipes. If you follow them….you’ll have a delicious ending!!

1. Solve for one variable in at least one equation, if necessary

2. Substitute the resulting expression into the other equation (circle and point to where substitution occurs)

3. Solve that equation4. Substitute the value into one of the original

equations and solve5. Write the values from Steps 3 and Steps 4 as

an ORDERED PAIR (x,y)

Helpful Hints

1. You can solve for x OR y2. Only ONE equation needs to be

solved for3. Use inverse operations correctly: Addition with subtraction Division with multiplication4. You should be SUBSTITUTING

twice5. CHECK YOUR ANSWERS!!!

y=2xy=x+5

Step 1: Done (both equations are solved for y

Step 2: y=x+52x=x+5

I put 2x in for y since y=2x

Step 3: -x from both sides

x=5

Step 4: y=2xy=2(5)y=10

Substitute found value into EITHER of the equations

Step 5: (5,10)

Write the solution as an ordered pair

Just Watch First!

Solve the system by substitution

y = 3x

y = x – 2

Step 1 y = 3xy = x – 2

Both equations are solved for y.

Step 2 y = x – 23x = x – 2

Substitute 3x for y in the second equation.

Solve for x. Subtract x from both sides and then divide by 2.

Step 3 –x –x2x = –22x = –22 2x = –1

Example #1

Step 4 y = 3x Write one of the original equations.

Substitute –1 for x. y = 3(–1)y = –3

Step 5 (–1, –3)Check Substitute (–1, –3) into both equations in the system.

Write the solution as an ordered pair.

y = 3x–3 3(–1)

–3 –3

y = x – 2–3 –1 – 2

–3 –3

y = x + 1

4x + y = 6

Step 1 y = x + 1 The first equation is solved for y.

Step 2 4x + y = 64x + (x + 1) = 6

Substitute x + 1 for y in the second equation.

Subtract 1 from both sides. Step 3 –1 –1

5x = 5 5 5

x = 1

5x = 5

5x + 1 = 6 Simplify. Solve for x.

Divide both sides by 5.

Example #2

Step 4 y = x + 1 Write one of the original equations.

Substitute 1 for x. y = 1 + 1y = 2

Step 5 (1, 2)Check Substitute (1, 2) into both equations in the system.

Write the solution as an ordered pair.

y = x + 1

2 1 + 12 2

4x + y = 6

4(1) + 2 66 6

You Try!

2x + y = -4

X + y = -7

–2x + y = 8

3x + 2y = 9Solve by substitution.

Solve the first equation for y by adding 2x to each side.

Step 1 –2x + y = 8+ 2x +2x

y = 2x + 8

Substitute 2x + 8 for y in the second equation. 3x + 2(2x + 8) = 9

3x + 2y = 9 Step 2

Distribute 2 to the expression in parenthesis.

3x + 2(2x + 8) = 9

Example #5Show all 5

steps!

Step 3 3x + 2(2x) + 2(8) = 9

7x + 16 = 9

Simplify. Solve for x.

Subtract 16 from both sides.

7x = –7

–16 –16

Divide both sides by 7.

7x = –77 7x = –1

3x + 4x + 16 = 9

Beeeeeee Careful!

Step 4 –2x + y = 8

Substitute –1 for x.

–2(–1) + y = 8

y + 2 = 8

–2 –2

y = 6

Step 5 (–1, 6) Write the solution as an ordered pair.

Subtract 2 from each side.

Simplify.

Write one of the original equations.

Almost Done!

Real World Application

Drew is deciding between two cell-phone plans. The first plan has a $50 sign-up fee and costs $20 per month. The second plan has a $30 sign-up fee and costs $25 per month. After how many months will the total costs be the same? What will the costs be? If Jenna has to sign a one-year contract, which plan will be cheaper? Explain.

Write an equation for each option. Let t represent the total amount paid and m represent the number of months.

Steal of a Deal!

Total paid is

sign-up fee plus

paymentamount

for eachmonth.

Option 1 t = $50 + $20 m

Option 2 t = $30 + $25 m

Step 1 t = 50 + 20mt = 30 + 25m

Both equations are solved for t.

Step 2 50 + 20m =30 + 25mSubstitute 50 + 20m for t in the second equation.

Setting it Up

Step 3 50 + 20m = 30 + 25m

Solve for m. Subtract 20m from both sides.–20m – 20m

50 = 30 + 5m Subtract 30 from both sides. –30 –30

20 = 5m Divide both sides by 5.

Write one of the original equations.

Step 4 t = 30 + 25m

t = 30 + 25(4)

t = 30 + 100

t = 130

Substitute 4 for m.Simplify.

5 5

m = 4

20 = 5m

Step 5 (4, 130)Write the solution as

an ordered pair.

In 4 months, the total cost for each option would be the same $130.

Drew should choose the first plan because it costs $290 for the year and the second plan costs $330.

Option 1: t = 50 + 20(12) = 290

Option 2: t = 30 + 25(12) = 330

If Drew has to sign a one-year contract, which plan will be cheaper? Explain.