Decide Model on Cereal
Autor: nicoleonfleek • July 17, 2019 • Essay • 408 Words (2 Pages) • 837 Views
Algebra 2
Writing Assignment: Systems of Equations
Each problem is worth 5 Points
Total Points: 50
Solve each system of equations. Show your work.
- -2x + 3y = 8
3x – y = -5
The equations are
3y=8+2x
and
y=3x+5
Multiplying the second equation by 3
3y=9x+15
Therefore,
8+2x=9x+15
Solving for x
7x=−7
x=−1
and
y=3x+5=3∗−1+5=2
The solutions are (-1,2)
- 4x - y = 8
-8x + 2y = -5
The equations are
y=4x−8
and
2y=8x−5
Multiplying the first equation by 2
2y=8x−16
Therefore
8x−5=8x−16
−5=−16
There are no solutions and the system is inconsistent.
- 5x + y = 13
3x = 15 – 3y
The equations are
y=−5x+13
and
3y=15−3x
Dividing the last equation by 3
y=5−3x
Therefore,
−5x+13=5−3x
Solving for x
2x=13−5=8
x=2
and
y=−5∗2+13=3
The system is consistent and has one solution (2,3)
- 2x + 4y = 36
10y = 5
The equations are
2x=36−4y
x=18−2y
and
10y=5
y=2
and
x=18−2∗2=18−4=14
The system is consistent and has one solution (14,2)
- 2x – 4y = 12 3x – 6y = 21
The equations are
2x=4y+12
That is
x=2y+6
and
3x=6y+21
That is
x=2y+7
Therefore,
2y+6=2y+7
6=7
The system has no solutions and is inconsistent.
- 2x – 9y = 32
4x + y = -12
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