# SOLUTION: HELP. Use elimination to solve each system of equations. 2X+2/3Y =4 X-1/2Y=7

Algebra ->  -> SOLUTION: HELP. Use elimination to solve each system of equations. 2X+2/3Y =4 X-1/2Y=7      Log On

 Ad: Mathway solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Click here to see ALL problems on Linear-systems Question 183031: HELP. Use elimination to solve each system of equations. 2X+2/3Y =4 X-1/2Y=7Answer by jim_thompson5910(29613)   (Show Source): You can put this solution on YOUR website! Start with the first equation. Multiply EVERY term by the LCD to clear any fractions. Distribute and multiply. ----------------------------------------------- Move onto the second equation. Multiply EVERY term by the LCD to clear any fractions. Distribute and multiply. So we have the system of equations: Multiply the both sides of the second equation by 2. 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. 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)