SOLUTION: Plz help me with this question: Solve using substitution to eliminate one variable. If the system has no solution, indicate that it is inconsistent,if it has infinite solutions,i

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Question 949234: Plz help me with this question:
Solve using substitution to eliminate one variable. If the system has no solution, indicate that it is inconsistent,if it has infinite solutions,indicate that it is Dependant,if the system has one solution,check your answer.
Y=-x+3
2x=-2y+10
Thanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=-x%2B3
2x=-2y%2B10
-----------------
x%2By=3
2x%2B2y=10
-----------------
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations

1%2Ax%2B1%2Ay=3
2%2Ax%2B2%2Ay=10

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.

Solve for y for the first equation

1%2Ay=3-1%2AxSubtract 1%2Ax from both sides

y=%283-1%2Ax%29 Divide both sides by 1.


Which breaks down and reduces to



y=3-1%2Ax Now we've fully isolated y

Since y equals 3-1%2Ax we can substitute the expression 3-1%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


2%2Ax%2B2%2Ahighlight%28%283-1%2Ax%29%29=10 Replace y with 3-1%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax%2B2%2A%283%29%2B2%28-1%29x=10 Distribute 2 to 3-1%2Ax

2%2Ax%2B6-2%2Ax=10 Multiply



2%2Ax%2B6-2%2Ax=10 Reduce any fractions

2%2Ax-2%2Ax=10-6 Subtract 6 from both sides


2%2Ax-2%2Ax=4 Combine the terms on the right side



0%2Ax=4 Now combine the terms on the left side.
0%2F1=4%2F1 Since this expression is not true, we have an inconsistency.


So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist.


+graph%28+500%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+%283-1%2Ax%29%2F1%2C+%2810-2%2Ax%29%2F2+%29+ graph of 1%2Ax%2B1%2Ay=3 (red) and 2%2Ax%2B2%2Ay=10 (green) (hint: you may have to solve for y to graph these)


and we can see that the two equations are parallel and will never intersect. So this system is inconsistent