solve using substitution method
3x-5y=61
3x-y=17
Substitute 3x-17 for y in the first equation and solve for x.
3x -15x +85 = 61
-12x = -24
Take it from there.
To solve the given system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable.
Let's solve the second equation, 3x - y = 17, for y.
Rearrange the equation to isolate y:
y = 3x - 17.
Step 2: Substitute the expression obtained from Step 1 into the other equation.
Substitute y = 3x - 17 into the first equation, 3x - 5y = 61:
3x - 5(3x - 17) = 61.
Step 3: Simplify and solve for x.
Expand the equation:
3x - 15x + 85 = 61.
Combine like terms:
-12x + 85 = 61.
Subtract 85 from both sides:
-12x = 61 - 85.
-12x = -24.
Divide both sides by -12:
x = -24 / -12.
x = 2.
Step 4: Substitute the value of x into one of the original equations and solve for y.
Substitute x = 2 into the second equation, 3x - y = 17:
3(2) - y = 17.
6 - y = 17.
Subtract 6 from both sides:
-y = 11.
Multiply both sides by -1 (or divide by -1):
y = -11.
Step 5: Verify the solution.
Substitute the values of x = 2 and y = -11 into both original equations:
Original equation 1: 3x - 5y = 61
3(2) - 5(-11) = 61
6 + 55 = 61
61 = 61
Original equation 2: 3x - y = 17
3(2) - (-11) = 17
6 + 11 = 17
17 = 17
The solution x = 2 and y = -11 satisfies both original equations.
Therefore, the solution to the given system of equations is x = 2 and y = -11.