System of Equations

1
System of Equations

• Elimination
• Using addition and subtraction
• S. Calahan

2
Addition

• Use elimination to solve the system of equations.
• 3x 5y -16
• 2x 5y 31
• Since the coefficients of the y terms,
• -5 and 5, are additive inverses, you can
  eliminate the y terms by adding the equations.

3
ADD

• 3x 5y -16
• 2x 5y 31
• 5x 15
• We canceled the y terms leaving only the x terms
  on the left hand side.

4
Now solve for x.

• 5x 15
• 5 5
• x 3
• Now lets solve for y.

5
Solve for y using substitution remember x 3

• 3x 5y -16
• 2x 5y 31
• Choose one of the original equations. 2x 5y
  31 and replace the x with 3.

6
Substitute and solve

• 2 (3) 5y 31
• 6 5y 31
• -6 -6
• 5y 25
• 5 5 so, y 5

7
Since x 3 and y 5

• The solution set for the equations
• 3x 5y -16
• 2x 5y 31
• is (3,5). This set of equations has only one
  solution.

8
Subtraction

• 5s 2t 6
• 9s 2t 22
• Since the coefficients of the t terms, 2 and 2,
  are the same, you can eliminate the t terms by
  subtracting the equations.

9
Add the opposite

• 5s 2t 6
• -(9s 2t 22) becomes
• 5s 2t 6
• -9s -2t -22

10
Now ADD

• 5s 2t 6
• -9s - 2t -22
• - 4s - 16
• Cancel the 2t and the -2t

11
Solve for s

• - 4s - 16
• - 4 - 4
• s 4
• Now solve for t

12
Substitute s 4 into an original equation and
solve for t

• 5s 2t 6
• 9s 2t 22
• Either equation will work. I will use
• 5s 2t 6 ,so 5(4) 2y 6

13
5s 2t 6 and s 4

• 5(4) 2t 6
• 20 2t 6
• -20 -20
• 2t -14
• 2 2 , then t -7.

14
Therefore, the solution set for

• 5s 2t 6
• 9s 2t 22
• is (4, -7).