# SOLUTION: x-4y=29 x-y=5

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 Question 202454: x-4y=29 x-y=5Found 2 solutions by jim_thompson5910, rfer:Answer by jim_thompson5910(28595)   (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) Answer by rfer(12662)   (Show Source): You can put this solution on YOUR website!x-4y=29 x-y=5 x=y+5 ------------ y+5-4y=29 -3y=24 y=-8 ----------- x-(-8)=5 x=-3 ---------- check -3-4(-8)=29 -3=32=29