Help. don't understand substitution method
also need an ordered pair?
7x+6y=15
-7x=y=27
http://www.helpalgebra.com/onlinebook/substitutionmethod.htm
I can help you understand the substitution method and find the ordered pair for the given equations.
The substitution method is a way to solve a system of equations by solving one equation for one variable and then substituting that expression into the other equation. Let's break it down step by step:
1. Start with the given system of equations:
7x + 6y = 15 (Equation 1)
-7x + y = 27 (Equation 2)
2. Solve one equation for one variable:
From Equation 2, we can rearrange it to solve for y:
y = 7x + 27
3. Substitute the expression for y into the other equation:
In Equation 1, replace y with 7x + 27:
7x + 6(7x + 27) = 15
4. Simplify and solve for x:
Distribute the 6 into the parentheses:
7x + 42x + 162 = 15
Combining like terms:
49x + 162 = 15
Subtract 162 from both sides:
49x = -147
Divide both sides by 49:
x = -3
5. Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Using Equation 2:
-7(-3) + y = 27
Simplify:
21 + y = 27
Subtract 21 from both sides:
y = 6
6. Finally, we have the ordered pair (x, y) as the solution to the system of equations. In this case:
(x, y) = (-3, 6)
To summarize, by using the substitution method, we found that the solution to the system of equations 7x + 6y = 15 and -7x + y = 27 is the ordered pair (-3, 6).