I am learning about substitutions. The equations are -3x+6y=4 and 2x+y=4.

Question

So I tried doing the equation out and I got fractions for the ordered pairs. I got x=4/3 and y=20/3. Our teacher has us do checks so when I checked the problem out it didn't work out. 

Answer 1

Let us work this step by step.

 

(i)  -3x + 6y = 4

(ii)  2x + y = 4

 

From (ii) get y = 4 - 2x and substitute into (i).  Then (i) becomes

 

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

-3x + 24 - 12x = 4

-15x = -20

x = -20/(-15) = 4/3

 

Then

 

y = 4 - 2x = 4 - 2(4/3) = 4 - 8/3 = (12 - 8)/3 = 4/3  [It looks like you made a mistake trying to find y.]

 

Test the solutions:

 

(i)  -3x + 6y = -3(4/3) + 6(4/3) = -12/3 + 24/3 = 12/3 = 4  [good]

(ii)  2x + y = 2(4/3) + (4/3) = 8/3 + 4/3 = 12/3 = 4 [good]