SOLUTION: For problems 5 and 6, solve the system of equations using SUBSTITUTION to eliminate one variable. If the system has no solution, indicate that is is inconsistent. If it has infin

Question 359617: For problems 5 and 6, solve the system of equations using SUBSTITUTION to eliminate one variable. If the system has no solution, indicate that is is inconsistent. If it has infinite solutions, indicate that it is dependent. If the system has a solution, CHECK YOUR ANSWER.
5.
y=2x
3x+y=20
CHECK (if possible)

6. 4x+2y=6
2x+y=3
CHECK (if possible)
I would really really appreciate help with this one because I don't really know what to do. Can someone help me, please?? Thanks so much!! :)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
For problems 5 and 6, solve the system of equations using SUBSTITUTION to eliminate one variable. If the system has no solution, indicate that is is inconsistent. If it has infinite solutions, indicate that it is dependent. If the system has a solution, CHECK YOUR ANSWER.
5.
y = 2x: this means we can substitute 2x for y in the 2nd equation, and find x
3x + y = 20
3x + 2x = 20
5x = 20
x = 4: divided both sides by 5
:
We know that y = 2x, therefore
y = 2(4)
y = 8
:
The solution x=4; y=8,
:
Check this in the 2nd equation
3x + y = 20
Substitute the values for x and y
3(4) + 8 = 20
12 + 8 = 20; equality checks the solutions
:
:
6. 4x + 2y =6
2x + y = 3
Rearrange this equation to use for substitution in the 1st equation
y = -2x + 3; subtracted 2x from both sides
:
Replace y with (-2x+3)in the 1st equation
4x + 2(-2x+3) = 6
4x - 4x + 6 = 6
4x - 4x = 6 - 6
0 = 0, dependent, an infinite number of solutions

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