SOLVE BY ELIMINATION METHOD

7r-8s+-20
8r+7s+74

Proofread your questions before you post them. We need two equations. There is no equal sign (=).

To solve the system of equations using the elimination method, follow these steps:

Step 1: Write both equations in standard form.
The given equations are:
Equation 1: 7r - 8s = -20
Equation 2: 8r + 7s = -74

Step 2: Multiply both sides of one or both equations by a constant so that the coefficients of one of the variables will be the same, but with opposite signs.

We observe that if we multiply Equation 1 by 8 and Equation 2 by 7, the coefficients of 'r' in both equations will become -64 and 56, respectively. This will allow us to eliminate the 'r' variable by adding or subtracting the two equations.

Multiplying Equation 1 by 8 gives:
8(7r - 8s) = 8(-20)
56r - 64s = -160

Multiplying Equation 2 by 7 gives:
7(8r + 7s) = 7(-74)
56r + 49s = -518

So, the modified equations become:
Equation 3: 56r - 64s = -160
Equation 4: 56r + 49s = -518

Step 3: Now, subtract the two equations to eliminate the 'r' variable.
Subtracting Equation 4 from Equation 3:
(56r - 64s) - (56r + 49s) = -160 - (-518)
56r - 64s - 56r - 49s = -160 + 518

Simplifying the equation:
-113s = 358

Step 4: Solve for 's' by dividing both sides of the equation by -113:
-113s / -113 = 358 / -113
s = -3.17 (rounded to two decimal places)

Step 5: Substitute the value of 's' back into one of the original equations to solve for 'r'.

Using Equation 1:
7r - 8(-3.17) = -20
7r + 25.36 = -20
7r = -45.36
r = -6.48 (rounded to two decimal places)

Therefore, the solution to the system of equations is r = -6.48 and s = -3.17.