Bell RingerSolve for x.

2x – 5 = 35 – 18x

Today’s LEQ:How do you solve a system of equations by substitution?

We already know we can solve a system of equations by graphing…

What might make graphing to solve a system difficult?

Not a nice y-intercept, the lines may

not intersect at a definite (x,y)

Solving Systems of Equations by Substitution – Part 1

Steps 

1.) _____________ an equation for either x or y. 2.) ________________________ your expression

into the _______________ equation to find the value of x or y.

 3.) ________________________ your value to find

the ______________ missing value of x or y.

Solve

Substituteother

Substituteother

Example

 y = -x + 10

y = 2x + 1Steps

1.) Solve an equation for either x or y.

2.) Substitute your expression into the other equation to find the value of x or y.

3.) Plug in your value to find the other missing value of x or y.

Let’s do some more….Find the solution to the system of equations by using substitution:

1. y = 3x + 5

y = -x + 13

Let’s do some more….Find the solution to the system of equations by using substitution:

2. x = -y + 10 x = 2y + 1

Let’s do some more….Find the solution to the system of equations by using substitution:

3. y = 2x y = 5x – 33

Let’s do some more….Find the solution to the system of equations by using substitution:

4. -3y = x x = -y + 14

Quick Check

Solve the system.

2 + 3y = x

x = -2y - 8

Now.….Help me solve the following equation for y.

2x – 8y = 24

Solving Systems of Equations by Substitution – Part 2

Steps 

1.) _____________ an equation for either x or y. 2.) ________________________ your expression

into the _______________ equation to find the value of x or y.

 3.) ________________________ your value to find

the ______________ missing value of x or y.

Solve

Substituteother

Plug inother

Example

 y = 2x – 2 3x + 2y = 38

Steps1.) Solve an equation for

either x or y.2.) Substitute your

expression into the other equation to find the value of x or y.

3.) Plug in your value to find the other missing value of x or y.

Let’s do some more….Find the solution to the system of equations by using substitution:

1. y = -4x 12x + y = 48

Let’s do some more….Find the solution to the system of equations by using substitution:

2. 2x = 4y x = 30 – 13y

Let’s do some more….Find the solution to the system of equations by using substitution:

3. x + y = 1 15 – 8y = x

Let’s do some more….Find the solution to the system of equations by using substitution:

4. 6x = 2y y = 4x – 4

Paper Quick Check(Graded?)