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how do you solve 2 different equations in the same problem

The problem is as follows. 
Y=4x
X+y=10

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I thank you. I failed algebra when I was in school and thought on how to help my daughter with her homework. I had solved the problem when I worked it but wanted to make sure I was actually doing it right.
The graphs of the equations are straight lines. The "solution" is the intersection of the two lines. There are 3 possibilities: one point (lines make an "X"), an infinite number of points (equations describe same graph), and no points (lines are parallel with no intersection).

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Robert C. | Effective Math and Science TutorEffective Math and Science Tutor
1
Hi Justin,
 
It states that y = 4x in your first equation. So plug 4x into where y is in the second equation.
 
x + y = 10 becomes x + 4x = 10. Which is simplified to 5x = 10 and then x = 2. 
 
Plug 2 in for x in the first equation to get y. y = 4(2) = y = 8
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
1
Hi Justin;
Y=4x
X+y=10
In the second equation, the x and y are on the left side.
Let's orient the first equation the same way...
y=4x
Let's subtract 4x from both sides...
-4x+y=0
-(x+y=10)
-5x+0=-10
We are subtracting the second equation from the first...
-5x=-10
x=2
Let's plug this into either equation to solve for y.  I randomly select the first equation...
y=4x
y=(4)(2)
y=8
Let's verify by plugging both results into the second equation...
x+y=10
2+8=10
10=10