x+y=4; y=3x solve both algebracially and graphically

Question

solve both problems algerbracially

Answer 1

To solve algebraically, you need to realize that the problem gives us a system of two equations (for two variables, x and y).

 

(1) x + y = 4

 

(2) y = 3x

 

So, we're looking for the ordered pair (x, y) that solves both (given that the two lines intersect).

 

Here's one way to do it:

 

Since we know from (2) that y = 3x, we can substitute this value of y for y in (1):

 

x + 3x = 4

 

4x = 4

 

x = 1

 

So, we now know the x-coordinate of the ordered pair.  To find y, substitute this value of x = 1 into either (1) or (2).

 

Let's do (2):

 

y = 3(1) = 3 so the y-coordinate is 3 and the ordered pair that solves both is:

 

(1, 3)

 

Hope this helps.