SOLUTION: I need help using the echelon method to solve each of two equations in two unknowns.
2x + 7y = -8
-2x + 3y = -12
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Question 147639This question is from textbook
: I need help using the echelon method to solve each of two equations in two unknowns.
2x + 7y = -8
-2x + 3y = -12
This question is from textbook
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:
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. Notice how the x terms cancel out.
Simplify.
Divide both sides by to isolate .
Reduce.
------------------------------------------------------------------
Now go back to the first equation.
Plug in .
Multiply.
Add to both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
So our answer is 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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