Transcript Solving Systems by Elimination cont.

Warm up 12/6 or 7
1) Write the equation of a line that is
parallel to y = -3x –5 and goes through
the point (6,10).
2) Write the equation of a line that is
perpendicular to y = -3x –5 and goes
through the point (6,10).
3) Using elimination, solve the following
system.
a) x + y = 4
-3x + y = -8
b) 3x – 4y = -15
5x + y = -2
Answers
to
warm
up
1) y = -3x + 28
2) Y = 1/3x +8
3) A) Subtract the two lines :
x+y=4
-3x + y = -8
4x = 12
(3, 1)
b) (-1, 3)
x = 3 Substitute: y = 1
Solving Systems by Elimination
cont.
Objective: To find the solution to
a system of equations by
elimination (addition).
Remember: The solution is the point
where the lines intersect.
1) 2x + 3y = 6
+5x – 4y = -8
4(2x + 3y) = 6(4)
3(5x – 4y) = -8(3)
We will need to change both
equations. We will have the y value
drop out.
8x + 12y = 24
+15x -12y = -24
23 x = 0
x=0
Now plug 0 in for x into any of the 4 equations.
2(0) + 3y = 6
The solution is (0, 2)
3y = 6
Y=2
You Try:
1. 2x + 3y = 14
(1, 4)
3x – 2y = -5
2. 5x + 2y = -8
2x – 5y = -9
(-2, 1)
Solve Systems by Elimination
This time both equations will be multiplied but one must be
multiplied by opposite sign to be canceled out.
Example 2) 4x+ 2y = -8
5x + 7y = 8
Step 1 – Choose one variable to eliminate. Let’s start with x.
One line will need to be multiplied by a negative number since all
coefficients are positive.
Let’s choose the first line.
-5(4x+ 2y) = -8(-5)
4(5x + 7y = 8(4)
-20x -10y = 40
20x + 28y = 32
18y = 72
y=4
Now substitute y back in to any of the four equations find x.
Example 2 Continued : 4x+ 2y = -8
5x + 7y = 8
4x + 2(4) = -8
4x + 8 = -8
-8
-8
4x = -16
X = -4
The solution is (-4,4)
YOU TRY!!
8x+ 2 y = 0
5x + 3y = -7
Answer: (1,-4)
Summary: What is the solution of a
system of linear equations?
Homework:7.4B WS