Solve the system by substitution. x + 3y = 6 and 2 x + y = 4?

Question

Solve the system by substitution.
x + 3y = 6
2 x + y = 4

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Thanks in Advance.

Answer 1

Isolate either the x or y of one problem. But only if that variable is by itself otherwise you'd have to divide it to get it by itself. In this case, it wouldn't matter if you isolated the x in the first problem or the y in the second. Isolating the y is more familiar, so I would do that.

2x + y = 4
-2x -2x
y = -2x + 4

So now you substitute that problem in x + 3y = 6.

x + 3 (-2x+4) = 6
x - 6x + 12 = 6
-5 x = -6
x = 6/5

Now substitute 6/5 for x in either of the problems.

6/5 + 3y = 6
3y = 24/5
y = 8/5

OR

2 (6/5) + y = 4
12/5 + y =4
y = 8/5

So the answer is (6/5, 8/5).

Answer 2

x + 3y = 6
2x + y = 4

multiply the second equation by -3:

x + 3y = 6
-3(2x + y = 4)

x + 3y = 6
-6x - 3y = -12

now add down:

-5x = -6
x = 6/5

now replace the x in either equation:

x+ 3y = 6
6/5 + 3y = 6

3y = 24/5

y = 24/15
y = 8/5


point of intersection: (6/5, 8/5)

Answer 3

x = 6 - 3y

12 - 6y + y = 4
- 5y = - 8
y = 8/5

x + 24/5 = 6
x = 6/5

x = 6/5 , y = 8/5

Answer 4

Here goes another one. To solve by substitution, you have to isolate one of the variables and then use that formula into the second equation. Isolate the x in the first equation, and after finding that equation, insert it into the second equation. Do it yourself, and report any problems. :)

Answer 5

point of intersection (1.2,1.6)