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)
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