What is the value of y, in terms of t, that would be in the solutions to the system below?

Question

5x+3y=9

10x+ty=-18

Answer 1

5x + 3y = 9           eq1

10x + ty = -18        eq2

 

 

First, multiply eq1 by 2.  Maintain eq2.

 

 

10x + 6y = 18          eq1

10x + ty = -18          eq2

 

 

Subtract eq2 from eq1 to eliminate the x terms.

 

 

6y - ty = 18 - (-18)

 

 

We will use this equation to solve for y in terms of t.  This means that y is on one side of the equation and t is on the other side of equation.

 

6y - ty = 36

 

 

Factor out the y on the left side of equation.

 

y(6 - t) = 36

 

 

Divide both sides of equation by (6 - t).

 

y = 36 / (6 - t)

 

 

 

 

 

Answer 2

Let's solve this system of equations using elimination. First, multiply the first equation by 2 to get:

 

2(5x + 3y = 9)

10x + 6y = 18

 

Now, subtract the second equation from the first equation to eliminate x:

 

      10x + 6y = 18

-   (10x + ty = -18)

----------------------------------

      0 + (6-t)y = 36

 

(6-t)y = 36

y = 36/(6-t)

 

Thus, the value of y in terms of t is y = 36/(6-t).