# SOLUTION: Solve the system by the addition (elimination) method. 2x+y=7 3x+y=12

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Solve the system by the addition (elimination) method. 2x+y=7 3x+y=12      Log On

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 Click here to see ALL problems on Linear-systems Question 187752This question is from textbook : Solve the system by the addition (elimination) method. 2x+y=7 3x+y=12This question is from textbook Answer by jim_thompson5910(28598)   (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 -1. 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. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. 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)