how would i solve this using the substitution method
3y=11-x
3x-y=3
thanks
Substitute 11 -3y for x in the second equation.
Why? Because the first equation tells you that
x = 11 -3y.
You should get
3(11 -3y)= 3 + y
33 - 9y = 3 + y
10y = 30
y = ___ ?
Then solve for x, using either of the first two equations you were given.
To solve the given system of equations using the substitution method, follow these steps:
1. Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, 3y = 11 - x, for y:
Divide both sides of the equation by 3:
y = (11 - x)/3
2. Substitute this expression for y into the other equation.
Substituting y = (11 - x)/3 into the second equation, 3x - y = 3:
3x - ((11 - x)/3) = 3
3. Simplify and solve the resulting equation for x.
To simplify, multiply both sides of the equation by 3 to eliminate the fraction:
3(3x) - (11 - x) = 3(3)
9x - 11 + x = 9
10x - 11 = 9
Add 11 to both sides of the equation:
10x = 9 + 11
10x = 20
Divide both sides of the equation by 10:
x = 20/10
x = 2
4. Substitute the value of x back into one of the original equations and solve for y.
Let's substitute x = 2 into the first equation, 3y = 11 - x:
3y = 11 - 2
3y = 9
Divide both sides of the equation by 3:
y = 9/3
y = 3
Therefore, the solution to the system of equations is x = 2 and y = 3.