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Solutions to systems and solving systems of equations using substitution

Study Slideshow

How many solutions does the system have?

Infinite

5

How many solutions does the system have?

No Solution

5

How many solutions does the system have?

One Solution

5

When solving a system of equations with substitution, your variables cancel out and you are left with -5 = 5. What is your solution?

No solution

10

When solving a system of equations with substitution, your variables cancel out and you are left with -3 = -3. What is your solution?

Infinite Solutions

10

What is the solution?

(1, -1)

10

Is the point (-7, 2) a solution to the system? y=x+9 and 3x+8y=-5

Yes

15

Is the point (-1, -2) a solution to the system? x=4y+7 and 2x-6y=12

No

15

Which equation would you rearrange in the system to solve by substitution? What does the equation look like when rearranged? 2x+y=-8 and 3x-5y=-25

First equation, y=-2x-8

15

Solve for x in the following system. x=4y and x+2y=12

x = 8

20

Solve for x in the following system. y=x-5 and x-7y=-1

x = 6

20

Solve for y in the following system. 3x-5y=-12 and y=-x-4

y = 0

20

Solve for y in the following system. 2x-5y=-22 and x+7y=27

y = 4

20

How should be write our final answers for a solution to the system?

Ordered Pair (x,y)

5

Solve the system of equations by substitution. x+y=15 and 4x+4y=10

No Solution

25

Solve the system of equations by substitution. 5x-4y=18 and x+y=-9

(-2,-7)

25