What happens if we graph a system of equations and the lines intersect, but we can’t tell exactly where they intersect?

Other than guessing, what could we do?

In this lesson you will learn how to solve a system of linear

equations by the addition/elimination method.

Let’s ReviewLet’s Review

X + 2 = 5

3(X + 2 = 5)

X + 2 = 5

3X + 6 = 15

Let’s ReviewLet’s Review

X + 2 = 5 3X + 6 = 15

-2 -2

X = 3

-6 -6

3X = 9

3 = 3

X = 3

Let’s ReviewCore Lesson

Determine the solution for the system of equations using the addition/elimination

method.x + y = 53x – y =7

x + y + 3x - y = 5 + 7

4x = 124 = 4

x = 3

Let’s ReviewCore Lesson

x + y = 53x – y =7

x = 3x + y = 53 + y = 5

-3 =-3 y = 2

The solution is (3,2)

Let’s ReviewA Common Mistake

Writing the solution in the form of first number found, second number found, rather than as (x,y)

Let’s ReviewCore Lesson

Check

3x – y = 7x + y = 5

The solution is (3,2)

3 + 2 = 5 5 = 5

3*3 – 2 = 7

7 =7

Let’s ReviewCore Lesson

Determine the solution for the system of equations the addition/elimination method.

x + y = 13x – 3y =7

x + y + x – 3y= 5 + 7

2x -2y = 12

Let’s ReviewCore Lesson

Determine the solution for the system of equations using the addition/elimination

method.

x + y = 13x – 3y =7

x + y = 13

-1(x – 3y = 7)

x + y = 13

-x + 3y = -7

Let’s ReviewCore Lesson

x + y = 13x + y -x + 3y= 13 - 7

4y = 6

-x + 3y = -7

4 = 4 y =

Let’s ReviewCore Lesson

x + y = 13x – 3y =7

x + y = 13 y =

x + = 13

- =-

x = The solution is (, )

Let’s ReviewCore Lesson

Checkx – 3y = 7x + y = 13

+ = 13

13 = 13

– 3* = 7

7 =7 The solution is (, )

Let’s ReviewCore Lesson

The solution is (, )

(, )

In this lesson you learned how solve a system of linear

equations by the addition/elimination method.

Let’s ReviewGuided Practice

Find the solution for the system of equations -x + y = 5 and x + 2y = 27 using the addition/elimination method.

Let’s ReviewGuided Practice

-x + y = 5 x + 2y = 27

Let’s ReviewGuided Practice

-x + y = 5 x + 2y = 27

Let’s ReviewGuided Practice

Find the solution for the system of equations x + y = -12 and 2x + y = 3 using the addition/elimination method.

Let’s ReviewGuided Practice

x + y = -12 2x + y = 3

Let’s ReviewGuided Practice

x + y = -12 2x + y = 3

Let’s ReviewExtension Activities

What property allows me to add these two equations together x + y =5 and x-y=2? Why?

Let’s ReviewExtension Activities

Find the solution of -3x+y=2 and 4x-y=4 using the addition/elimination method.

Let’s ReviewExtension Activities

Create a system of linear equations that have only one solution. Solve the equations by using the addition/elimination method.

Let’s ReviewQuick Quiz

The solution for the system of linear equations x-2y = -9 and x + 3y = 16 isa)(-1, 5) b) (1, -5) c) (1, -5) d) (-1,-5)

The solution for the system of linear equations 2x + y = 9 and 3x - y = 16 isa)(5, -1) b) (-5, 1) c) (-5, -1) d) (5,5)