SOLUTION: Solve the system by the addition method. Determine whether the equations are independent, dependent, or inconsistent.
3x - 2y = -7
x – 5y = 2
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Question 207149: Solve the system by the addition method. Determine whether the equations are independent, dependent, or inconsistent.
3x - 2y = -7
x – 5y = 2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:
Multiply the both sides of the second equation by -3.
Distribute and multiply.
So we have the new system of equations:
Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms.
Simplify.
Divide both sides by to isolate .
Reduce.
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Now go back to the first equation.
Plug in .
Multiply.
Subtract from both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
So the solutions are and .
Which form the ordered pair )
.
This means that the system is consistent and independent.
Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.
Graph of (red) and (green)
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