Question

and [6.03] What is the value of the x variable in the solution to the following system of equations?

4x + y = 8
x − 2y = 2

0

2

There is no x value as there is no solution to this system

x can be any value as there are infinitely many solutions to this system

Answer 1

Solve the equations.

4x + y = 8
y = 8 - 4x

x - 2y = 2
x - 2 = 2y
y = (x - 2)/2

y = y, therefore:
(x - 2)/2 = 8 - 4x
x - 2 = 16 - 8x
x + 8x = 16 + 2
9x = 18
x = 18/9
x = 2

That leaves answer B or D. Rule out D by putting x = 0 into the equations:

4(0) + y = 8
y = 8
and
0 - 2y = 2
2y = 2
y = 1

Since y = y, and 8 = 1 is not correct, there are not infinitely many solutions, and since x is not dependent on an exponent, the solution cannot be -2, so the solution is 2 and only 2, so the answer is B.

Answer 2

wow! thanks so much!

Answer 3

No problem. Just realized I made a mistake there at the end:

0 - 2y = 2
2y = 2
y = 1

should be:

0 - 2y = 2
-2y = 2
y = -1

Answer 4

haha