Question 120131: 7x-y=10
x=2y-6
I have to solve this problem using substitution and I don't understand and I'm really confused could someone please help me? Found 2 solutions by jim_thompson5910, Earlsdon:Answer by jim_thompson5910(35256) (Show Source):
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Distribute
Combine like terms on the left side
Add 42 to both sides
Combine like terms on the right side
Divide both sides by 13 to isolate y
Divide
Now that we know that , we can plug this into to find
You can put this solution on YOUR website! Solv by the substitution method:
1)
2)
The idea behind the subtitution method of solving systems of equations, such as you have here, is to eliminate one of the two variables (x or y) so that you will have one equation with one unknown.
Notice that equation 2) is conveniently written in terms of the variable x, that is, you have the variable x isolated on the left side while everything else is on the right side. This means that you can substitute the x in equation 1) with the x = 2y-6 of equation 2), then you will have equation 1) with only one variable (y) in it.
1a) Simplify this. Combine like-terms. Add 42 to both sides. Divide both sides by 13. Now you can substitute this value of y into either one of the two original equations to solve for the other variable, x. Let's use equation 2) for this. Substitute y = 4.
So the solution is: (2, 4)
Remember that the solution to a system two linear equations is the point of intersection of the two lines represented by the two equations,, if there is one.
Let's look at the graph of the two equations and you'll see what I mean:
(