solve each system of equations by substitution.
y=3x-9
please help explain how to solve this using substitution.
A single equation is not a system of equations.
To solve this system of equations using substitution, we need to substitute the value of one variable from one equation into the other equation. Here's a step-by-step explanation of how to do it:
Step 1: Begin with the given system of equations:
y = 3x - 9 ---(Equation 1)
Step 2: Choose one of the equations (in this case, Equation 1) and solve it for one variable in terms of the other. In this equation, y is already isolated. Therefore, we don't need to make any changes.
Step 3: Substitute the expression for the variable from Step 2 into the other equation. Since the expression for y is already given in Equation 1, we'll substitute it into the second equation.
Substituting y = 3x - 9 into the second equation, we get:
5x - 4(3x - 9) = 2
Step 4: Simplify the equation obtained from Step 3.
Distribute the -4 over the terms inside the parentheses:
5x - 12x + 36 = 2
Combine like terms:
-7x + 36 = 2
Step 5: Solve the equation from Step 4 for the remaining variable.
Subtract 36 from both sides of the equation:
-7x = 2 - 36
-7x = -34
Divide both sides by -7 to isolate x:
x = -34 / -7
x = 4.857
Step 6: Substitute the value of x back into one of the original equations to find the corresponding value of y.
Using Equation 1, substitute x = 4.857:
y = 3(4.857) - 9
y = 14.571 - 9
y = 5.571
Step 7: Write the solution as an ordered pair (x, y).
The solution to the system of equations is (4.857, 5.571).