Question

What is the difference of the values of the two variables in this system of equations?

y = 2x + 1
x + 3y = 10
a) 0
b) 1
c) 2
d) 3

Answer 1

By substituting the expression for y into the second equation and solving for x, we find x = 1. Plugging x into the first equation gives us y = 3. The difference between y and x is 2 (y - x = 3 - 1), so the correct answer is (c) 2.

Step-by-step explanation:

To find the difference of the values of the two variables in the given system of equations, we need to solve the equations simultaneously. We have the equations y = 2x + 1 and x + 3y = 10.

First, substitute the expression for y from the first equation into the second equation:

x + 3(2x + 1) = 10

x + 6x + 3 = 10

7x + 3 = 10

Subtract 3 from each side:

7x = 7

Divide each side by 7:

x = 1

Now substitute x = 1 into the first equation to find y:

y = 2(1) + 1

y = 2 + 1

y = 3

The difference between y and x is:

y - x = 3 - 1

The difference is 2.

Therefore, the correct answer is (c) 2.