Solve the equation by the substition method. x-y=11 3x+10y=-6?
To solve the given system of equations by the substitution method, we need to solve one of the equations for one variable and substitute the expression into the other equation.
Given equations:
1) x - y = 11
2) 3x + 10y = -6
Step 1: Solve equation (1) for x or y.
Let's solve equation (1) for x:
x = y + 11
Step 2: Substitute the expression for x from equation (1) into equation (2).
Replace x in equation (2) with (y + 11):
3(y + 11) + 10y = -6
Step 3: Simplify and solve the resulting equation.
Distribute 3 to (y + 11):
3y + 33 + 10y = -6
Combine like terms:
13y + 33 = -6
Subtract 33 from both sides:
13y = -6 - 33
13y = -39
Divide both sides by 13:
y = -39/13
y = -3
Step 4: Substitute the found value of y back into equation (1) to solve for x.
x = y + 11
x = -3 + 11
x = 8
Therefore, the solution to the system of equations is x = 8 and y = -3.