my question is this how do you solve this equation?
x=3y-1
x+2y=9
solve each system of equation by the substitution method.
Substitute 3y -1 for x in the second equation, and solve the resulting equation for y
3y -1 + 2y = 9
which leads to
5y = 10
Take it from there
(3y-1) + 2y = 9
5y - 1 = 9
5y = 10
y=2
x=3(2)-1
x=5
(5,2)
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable.
We have two equations:
Equation 1: x = 3y - 1
Equation 2: x + 2y = 9
In Equation 1, isolate the variable x:
x = 3y - 1
Step 2: Substitute the expression for x in the other equation.
Substitute (3y - 1) for x in Equation 2:
(3y - 1) + 2y = 9
Step 3: Solve the resulting equation.
Combine like terms:
3y + 2y - 1 = 9
5y - 1 = 9
Add 1 to both sides of the equation:
5y - 1 + 1 = 9 + 1
5y = 10
Divide both sides by 5:
5y/5 = 10/5
y = 2
Step 4: Substitute the value of y back into one of the original equations.
We'll use Equation 1:
x = 3y - 1
x = 3(2) - 1
x = 6 - 1
x = 5
Step 5: Verify the solution.
Substitute the obtained values for x and y into the second equation:
x + 2y = 9
5 + 2(2) = 9
5 + 4 = 9
9 = 9
Since the equation is true, the solution is valid.
Therefore, the solution to the system of equations is x = 5 and y = 2.