Transcript Solving Systems by Elimination

Lesson 7.4A
Solving Linear Systems Using
Elimination
Keys to Know
Solving with Elimination:
When you combine the equations to get rid of
(eliminate) one of the variables.
Possible solutions are:
One Solution
No Solutions
Infinite Solutions
Steps for Using Elimination
1)
2)
3)
4)
5)
6)
7)
Write both equations in standard form
(Ax + By = C) so that variables and = line up
Multiply one or both equations by a number to make
opposite coefficients on one variable.
Add equations together (one variable should cancel
out)
Solve for remaining variable.
Substitute the solution back in to find other variable.
Write the solution as an ordered pair
Check your answer
Example 1:
5x + y = 12
3x – y = 4
8x
= 16
8
8
x=2
5(2) + y = 12
10 + y = 12
y=2
The solution is: (2, 2)
Step 1: Put both equations in
Already Done
standard form.
Step 2: Check for opposite y and –y are
already
coefficients.
opposites
Step 3: Add equations
together
Step 4: Solve for x
Step 5: Substitute 2 in for x to
solve for y (in either equation)
Your Turn
Ex. 2 2x + y = 0
-2x + 3y = 8
Answer: (-1, 2)
When we need to create opposite
coefficients
Example 3
3x + 5y = 10
3x + y = 2
3x + 5y = 10
-1(3x + y) = -1(2)
When you add these neither variable drops out
SO….
We need to change 1 or both equations by
multiplying the equation by a number that will create
opposite coefficients.
3x + 5y = 10 Multiply the bottom
equation by negative one
to eliminate the x
-3x – y = -2
4y = 8
y=2
Now plug (2) in for y.
3x + 2 = 2
X=0
Solution is : (0,2)
4) -2x + 3y = 6
x – 4y = -8
-2x + 3y= 6
2( x – 4y) = -8(2)
We will need to change both
equations. We will have the y value
drop out.
-2x + 3y = 6
2x - 8y = -16
-5 y = -10
y=2
Now plug (2) in for y into any of the 4 equations.
-2x + 3(2) = 6
-2x + 6 = 6
-2x = 0
x=0
Solution is: (0, 2)
Check your work!
Your Turn
Ex. 5
5x – 2y = 12
2x – 2y = -6
(6, 9)
Ex. 6
-3x + 6y = 9
x - 2y = -3
0=0
Infinite
solutions
Ex. 7
2x + 4y = 8
x + 2y = 3
0=2
No
Solutions