Which ordered pair is the solution to the system of equations below using the substitution method?

Question

3x+2y=16

4x-5y=6

 

A. (4,2)

B. (3,5)

C. (2,6)

D. (5,4)

Answer 1

To use the substitution method, we must isolate a variable for one of the two given equations. I'll isolate y for the first equation:

 

3x+2y=16

2y=16-3x

y=8-(3/2)x

 

Now, we can use this value to plug into the second equation:

 

4x-5y=6

y=8-(3/2)x

4x-5[8-(3/2)x]=6

 

From here, use algebra to simplify the equation:

 

4x-(5)(8)-5[-(3/2)x]=6

4x-40+(15/2)x=6

4x+(15/2)x=46

(8/2)x+(15/2)x=46

(23/2)x=46

(23/2)x*2=46*2

23x=92

x=92/23

x=4

 

Lastly, we can plug our x-value back into the other original equation to find the value for y.

 

3x+2y=16

x=4

3(4)+2y=16

12+2y=16

2y=4

y=4/2

y=2

 

Finally, given the choices and our knowledge of how to write (X,Y) coordinates, we know that the answer must be A: (4,2).