Solve the following system using the substitution method:
y = 3x - 9
y = -x - 1
To solve the system of equations using the substitution method, we need to find the value of one variable and substitute it into the other equation.
Let's solve the system step by step:
Step 1: We will start by solving one of the equations for one variable (preferably the simplest one). Let's solve the second equation for y.
Given y = -x - 1, we will write this equation as:
y = -1x - 1
Step 2: Now, we substitute the expression for y from the second equation into the first equation.
Substituting -1x - 1 for y in the first equation, we have:
-1x - 1 = 3x - 9
Step 3: Simplify and solve the equation for x.
Let's rearrange the equation and collect the variables on one side:
-1x - 3x = -9 + 1
Combining like terms, we get:
-4x = -8
Divide both sides of the equation by -4 to solve for x:
x = -8 / -4 = 2
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using the first equation y = 3x - 9, substitute x = 2:
y = 3(2) - 9
y = 6 - 9
y = -3
Step 5: Check the solution.
Plug the values of x = 2 and y = -3 into both equations:
Equation 1: y = 3x - 9
-3 = 3(2) - 9
-3 = 6 - 9
-3 = -3
Equation 2: y = -x - 1
-3 = -(2) - 1
-3 = -2 - 1
-3 = -3
The solution is x = 2 and y = -3.
Thus, the solution to the system of equations y = 3x - 9 and y = -x - 1 is x = 2 and y = -3.
x=2
y=-3