Elimination To solve systems by elimination

The goal in solving a system is to eliminate the 2 equations with 2 unknowns (variables) to 1 equation with 1 unknown.

1.Put both equations in standard form 2.Determine which variable you want to "eliminate" hint: Look for a variable that has the same coefficient in both equations or opposites (i,e 2a and 2a or 2a and -2a) 3. Rules for elimination if the signs are the same, then you need to subtract If the signs are opposite, you need to add 4. Once a variable is eliminated, solve for the other variable 5. Substitute solution back into one of the original equations to find the other variable

2a + 4( ) = 30 Same coefficient and same sign so I need to subtract 2a + 4c = 30 2a + 2c = c = 20 c = 10 Substitute 10 into 1 of the original equations and solve 10 2a + 40 = 30 2a = -10 a = -5 (-5,10) common mistake is to not subtract every term in 2nd eq from the 1st

2x + 3y = -11 2x + 5y = -25 questions to ask yourself? Do I have any coefficients that are the same? - same sign so I need to subtract! Don't forget to subtract every term! -2y = 14 y = -7 now what do I do? Oh yeah, substitute in to find my other value 2x + 3(-7) = -11 2x = -11 2x = 10 x = 5 How do I finish this off? Oh yeah as an ordered pair. (5, -7) I think I got it. Let me try again.

4x + 2y = 10 3x - 2y = 4 + 7x = 14 x = 2 4(2) + 2y = y = 10 2y = 2 y= 1 (2,1)

-3x + 4y = 12 3x - 6y = y = 30 y = -15 3x - 6(-15) = 18 3x + 90 = 18 3x = -72 x = -24 (-24,-15)

Steps: 1. decide which variable to eliminate 2. make coefficients the same by using mult. 3. Solve just like the previous problems

2x + 3y = 5 5x + 4y = 16 4[ ] 3[ ] 8x + 12y = 20 15x + 12y = 48 (-) -7x = -28 x = 4 2(4) + 3y = y = 5 3y = -3 y = -1 (4, -1)

4x + 3y = 8 3x - 5y = -23 [ ] 5 [ ]3 20x + 15y = 40 9x - 15y = x = -29 x = -1 4(-1) + 3y = y = 8 3y = 12 y = 4 (-1,4)