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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

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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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