solve the system of equations 2r+2s = 50 and 2r-s=17

2r+2s = 50

2r-1s = 17
----------- subtract
0r+3s = 33
s = 11 You can now find r

To solve the system of equations 2r + 2s = 50 and 2r - s = 17, we can use the method of substitution.

Step 1: Solve one equation for one variable in terms of the other variable.

Let's solve the second equation, 2r - s = 17, for s:
2r - s = 17
Simplify: -s = 17 - 2r
Multiply both sides by -1 to isolate s: s = -17 + 2r

Step 2: Substitute the expression for s into the other equation.

Now, substitute the expression for s into the first equation, 2r + 2s = 50:
2r + 2(-17 + 2r) = 50
Simplify: 2r - 34 + 4r = 50
Combine like terms: 6r - 34 = 50
Add 34 to both sides: 6r = 84
Divide both sides by 6: r = 14

Step 3: Substitute the value of r back into one of the original equations to solve for the other variable.

Substituting r = 14 into the second equation, 2r - s = 17:
2(14) - s = 17
Simplify: 28 - s = 17
Subtract 28 from both sides: -s = -11
Multiply both sides by -1 to isolate s: s = 11

So, the solution to the system of equations 2r + 2s = 50 and 2r - s = 17 is r = 14 and s = 11.