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# Systems of Linear Equations

Please assist to understand the difference in these different methods. Please show work so I can follow the solution.

Determine if the given ordered pair is a solution to the system:

12. 2x + y = 5 (4, -3)
x - y = 1

22. 4x - y = -2 (-1, -2)
3x + y = -5

Solve each system of equations by the graphing method:

32. x - y = 4
x + y = 2

48. -4x + 4y = 4
y = x + 1

Solve each system of equations by the substitution method:

52. 8x + 3y = -14
-x + 2y = -3

66. -3x + 2y = 8
y = 3/2x + 3

Solve each system of equations by the addition method:

74. 3x + 5y = 4
-4x + 2y = -1

88. 6x + 2y = 8
2x - y = 6

#### Solution Preview

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Determine if the given ordered pair is a solution to the system:

12. 2x + y = 5 (4, -3)
x - y = 1

Solution. As 4-(-3)=4=3=7, we know that (4, -3) does not satisfy the 2nd equation x-y=1. So, it is not a solution to the system.

22. 4x - y = -2 (-1, -2)
3x + y = -5
Solution. As

4*(-1)-(-2)=-4+2=-2
and
3*(-1)+(-2)=-3-2= -5,
we know that (-1, -2) does satisfy the 1st and 2nd equations. So, it is a solution to the system.

Solve each system of equations by the graphing ...

#### Solution Summary

Systems of linear equations are solved by addition and graphing. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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