solve by elimination
5r-3s=19
2r-6s=-2
5 r - 3 s = 19 Multiply both sides by - 2
- 5 r * ( - 2 ) - 3 s * ( - 2 ) = 19 * ( - 2 )
- 10 r + 6 s = - 38
Now your system become:
- 10 r + 6 s = - 38
+
2 r - 6 s = - 2
__________________
- 10 r + 2 r + 6 s - 6 s = - 38 + ( - 2 )
- 8 r = - 38 - 2
- 8 r = - 40 Divide both sides by - 8
r = - 40 / - 8 = 5
r = 5
5 r - 3 s = 19
5 * 5 - 3 s = 19
25 - 3 s = 19 Subtract 25 to both sides
25 - 3 s - 25 = 19 - 25
- 3 s = - 6 Divide both sides by - 3
s = - 6 / - 3 = 2
s = 2
Solution:
r = 5 , s = 2
5 r - 3 s = 19 Multiply both sides by - 2
5 r * ( - 2 ) - 3 s * ( - 2 ) = 19 * ( - 2 )
- 10 r + 6 s = - 38
To solve the system of equations using the method of elimination, follow these steps:
Step 1: Multiply Equation 1 by 2 and Equation 2 by 5 to make the coefficients of 'r' in both equations the same (10r):
2(5r - 3s) = 2(19) ----> 10r - 6s = 38 (Equation 3)
5(2r - 6s) = 5(-2) ----> 10r - 30s = -10 (Equation 4)
Step 2: Now, subtract Equation 4 from Equation 3 to eliminate the term with 'r':
(10r - 6s) - (10r - 30s) = 38 - (-10)
10r - 6s - 10r + 30s = 38 + 10
Step 3: Simplify and solve for 's':
-6s + 30s = 48
24s = 48
s = 48/24
s = 2
Step 4: Substitute the value of 's' into one of the original equations (Equation 1 or Equation 2) and solve for 'r'. Let's use Equation 1:
5r - 3(2) = 19
5r - 6 = 19
5r = 19 + 6
5r = 25
r = 25/5
r = 5
Therefore, the solution to the system of equations is r = 5 and s = 2.