substitution for 5r-s=5 -4r+5s=17
Rearrange first equation.
s = 5r - 5
-4r + 5s = 17
Substitute 5r - 5 for s in the second equation and solve for r. Put that value in the first equation to solve for s. Check by putting both values in the second equation.
To find the substitution for the system of equations:
1) Let's solve the first equation, 5r - s = 5, for s:
Subtract 5r from both sides of the equation:
-s = -5r + 5
Multiply through by -1 to make s positive:
s = 5 - 5r
2) Now, substitute this value of s into the second equation, -4r + 5s = 17:
-4r + 5(5 - 5r) = 17
Simplify:
-4r + 25 - 25r = 17
Combine like terms:
-29r + 25 = 17
Subtract 25 from both sides of the equation:
-29r = -8
Divide through by -29 to find the value of r:
r = -8 / -29
Simplify the fraction if needed.
By substituting the value of r back into the original equation, you can solve for s.
To solve the system of equations:
1) 5r - s = 5
2) -4r + 5s = 17
We can use the method of substitution. Here's how you can proceed:
Step 1: Solve equation 1 for one variable. We will solve for r in terms of s.
Add s to both sides of equation 1:
5r - s + s = 5 + s
5r = 5 + s
Divide both sides by 5:
r = (5 + s) / 5
Step 2: Substitute the expression for r from equation 1 into equation 2.
Replace r in equation 2 with (5 + s) / 5:
-4((5 + s) / 5) + 5s = 17
Step 3: Simplify and solve for s.
Distribute -4 to (5 + s):
-4 * 5/5 - 4s/5 + 5s = 17
-4 - 4s/5 + 5s = 17
Multiply both sides by 5 to eliminate the denominator:
-20 - 4s + 25s = 17 * 5
Combine like terms:
21s - 20 = 85
Add 20 to both sides:
21s = 105
Divide both sides by 21:
s = 105/21
s = 5
Step 4: Substitute the value of s back into equation 1 to solve for r.
Replace s with 5 in equation 1:
5r - 5 = 5
Add 5 to both sides:
5r = 10
Divide both sides by 5:
r = 2
Therefore, the solution to the system of equations is r = 2 and s = 5.