Solve the equation by the substition method. x-y=11 3x+10y=-6?
first equation: x-y=11 ---> x = y+11
sub into 2nd
3x + 10y = -6
3(y+11) + 10y = -6
3y + 33 + 10y = -6
13y = -39
y = -3 , then
x = -3+11 = 8
To solve the given system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, x - y = 11, for x.
Adding y to both sides of the equation, we get:
x = y + 11
Step 2: Substitute the expression found in Step 1 into the second equation.
Substituting x from Step 1 (x = y + 11) into the second equation 3x + 10y = -6, we get:
3(y + 11) + 10y = -6
Step 3: Simplify and solve the resulting equation.
Distribute the 3 to y and 11:
3y + 33 + 10y = -6
Combining like terms:
13y + 33 = -6
Subtracting 33 from both sides:
13y = -39
Dividing by 13:
y = -3
Step 4: Substitute the found value of y back into one of the original equations to find the value of x.
Let's substitute y = -3 into the first equation, x - y = 11:
x - (-3) = 11
x + 3 = 11
Subtracting 3 from both sides:
x = 8
Therefore, the solution to the given system of equations is x = 8 and y = -3.