Notes Sys Eq Substitution

Notes Sys Eq Substitution

Substitution

We have already encountered substitution

3x+2 when x=5

to evaluate the expression above we substitute 5 for x and get

3(5)+2

Remember 3x means multiply

3 times 5 + 2 equals 17

Multiple Choice

Work out the value of the following expressions when a = 3 and b = 4.

a + b

• 7

• 8

• 9

• 6

Multiple Choice

In the expression

3x + 2

3x is which operation?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

Work out the value of the following expressions when a = 3.

2a

• 5

• 6

• 8

• 10

Multiple Choice

Work out the value of the expression when x = 3, y and z = – 4.

2xz

• 1

• 24

• -24

• 9

Work the next three on your own

Multiple Choice

If y=7,find the value of 2(y+4)

• 11
• 22
• 20
• 18

Multiple Choice

Work out the value of the expression when x = 3, y = – 2 and z = – 4.
y + x – z     

• -5
• -3
• 3
• 5

Multiple Choice

Work out the value of the following expressions when a = 3 and b = 4.

3ab

• 10

• 12

• 15

• 36

Substitution with two variables

When we have two variables we need two equations.

You can solve for one variable and substitute that into the other variable.

y = 2x

4x + 3y = 10

In the first equation, we see that y=2x. We substitute 2x for y in the second equation.

4x+3(2x)=10 Now we can solve for one variable x

4x+ 6x = 10 Combine like terms (x)

10x = 10 Inverse operation to isolate the variable. Divide by 10

x = 1 we also know y=2x from the first equation, so y=2(1)=2

(x,y) = (1,2)

Multiple Choice

What is the solution to the following system?

^{x - y = 6}

^{x = 11}

• (11, 5)

• (55, 5)

• (11, 11)

• (5, 55)

Multiple Choice

y = -6
-3x - 6y = 24

• (6, 6)
• (6, -6)
• (4, -6)
• (-6, 4)

Multiple Choice

Solve the system of equations.

• (-34, -17)

• (8, 4)

• (10, 20)

• No solution

• Infinite solutions

Multiple Choice

Solve the following systems of equations using substitution:

x = 6

y = 2x - 3

• (6, 6)

• (6, 9)

• (9, 6)

• (9, 9)

Multiple Choice

Solve the system of equations.

• (-6, 1)

• (0, 0)

• (1, -6)

• No solution

• Infinite solutions

Multiple Choice

solve by substitution: y=3x+14
y=-4x

• y=3
• y=1
• y= - 2
• y=4

Multiple Choice

Solve the following systems of equations using substitution:

5x - 2y = 3

y = 2x

• (6, 3)

• (1, 2)

• (3, 6)

• (2, 1)

Multiple Choice

y = -2x + 18
y = 8

• (5, 8)
• (-5, 8)
• (2, 8)
• (-2, 8)

Solutions

One solution ex. x=1 y=2 (1,2)

variable = number

No solution 3=4 or 2=5

variable goes away, numbers are not equal

number = different number

Infinite Solutions

variable goes away and numbers are equal

3=3 etc.

Multiple Choice

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

Multiple Choice

What is the solution to the system?

• (3, -1)
• (2, -6)
• No Solution 
• (6, -2)

Multiple Choice

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Multiple Choice

Determine the type of solution you will have if you get
4=8

• one solution
• infinite solution=identity
• no solution
• I don't know.  I need to study.

Multiple Choice

Determine the type of solution you will have if you get
5=3

• one solution
• infinite solution=identity
• no solution
• I don't know.  I need to study.

Multiple Choice

Determine the type of solution you will have if you get
-5=-5

• one solution
• infinite solution=identity
• no solution
• I don't know.  I need to study.

Multiple Choice

Determine the type of solution you will have if you get
w=-5

• one solution
• infinite solution=identity
• no solution
• I don't know.  I need to study.

Multiple Choice

Determine the type of solution you will have if you get
4=4

• one solution
• infinite solution=identity
• no solution
• I don't know.  I need to study.

Multiple Choice

What is the solution to the following system?

^{y = 3x}

^{12x - 4y = 20}

• (0, 0)

• no solutions

• (0, 20)

• infinite solutions

Solving Systems of equations with substitution

Solve for one variable

Substitute into the other variable

Solve for one variable

Multiple Choice

Solve the following system:

 $y=-2$  

 $4x-3y=18$  

•  $\left(3,\ -2\right)$  

•  $\left(3,\ 2\right)$  

•  $\left(-2,3\right)$  

•  $\left(2,\ 3\right)$  

Multiple Choice

Solve the following system:

 $y=5x-7$  

 $-3x-2y=-12$  

•  $\left(2,\ 3\right)$  

•  $\left(3,\ 2\right)$  

•  $\left(-2,\ -3\right)$  

•  $\left(-2,\ 3\right)$  

Multiple Choice

Solve the following system:

 $2x-y=-1$  

 $y=x-1$  

•  $\left(-2,-3\right)$  

•  $\left(4,\ 5\right)$  

•  $\left(5,\ 3\right)$  

•  $\left(3,\ 4\right)$