Solving Systems of Equations by Graphing
1st Equation: 2X-3Y=2 : 2nd Equation: X+2Y=15
Substitution:1) Find the easiest equation to get a variable alone
2) In the 2nd equation you could easily get X alone 3) Subtract 2Y from the other side of the equals sign 4) X = 15 - 2Y 5) Substitute 15 - 2Y for the X in the first equation 6) 2 (15-2Y) - 3Y = 2 7) Distribute: 30 - 4Y - 3Y = 2 8) Combine like-terms: -7Y = -28 9) Solve for Y: Y = 4 10) Plug in Y: X = 15 - 2 (4) = 7 |
Elimination:1) Find a common number to multiply each equation by
2) Multiply 1st equation by 2 and 2nd by 3 3) 4X - 6Y =4 : 3X + 6Y = 45 4) Combine the two equations 5) Eliminate Y: 7X = 49 6) X = 7 7) Plug in X: (7) + 2Y = 15 8) Y = 4 9) Either system you chose to use, the results are the same 10) (7,4) |
*Graph the point (7,4) which is the point of intersection*