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Systems of Equations Substitution and Addition Methods

Solve the following system by graphing:

14.
x - 2y = -6
y = -3x/2 - 1

15.
y < 5x - 2
y > 3x - 2

Solve the following systems by the addition method:

16.
x + 2y = 4
3x - 6y = 6

17.
4x - 5y = 20
y = 4/5x - 4

Solve the following systems by the substitution method:

18.
7x - 4y = 26
y = x - 5

19.
4x + y = 7
3x - y = 0

20.
x - 2y = 0
4x - 8y = 0

Solution Preview

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Solve the following system by graphing:

14. x - 2y = -6
y = -3x/2 - 1

To solve these problems,
1) convert both equations to lines of the form y = mx + b.
2) find 2 points for each line
3) Graph the lines
4) The intersection point will be the solution.

y = -3x/2 - 1 is ok
x y
0 -1
1 -2.5

x - 2y = -6
2y = x + 6
y = (1/2)x + 3

X y
0 3
1 3.5

The intersect is (-2,2)
Checking...
x - 2y = -6
y = -3x/2 - 1

-2 - (2 x 2) = -6 ...yes
2 = -(3 x -2)/2 - 1...yes

15. y < 5x - 2
y > 3x - 2

Graph each line and figure out the common area.

The "common area" is the intersection between the area below (<=) y = 5x -2 and
above (>=) y = 3x - 2. ...

Solution Summary

Systems of Equations are solved using Substitution and Addition/Elimination Methods. Full working is shown.

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