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 solving the system of equations using substitution, the value of x is found to be 1, and the value of y is 3. The difference between the values of x and y is 2.

Step-by-step explanation:

The question asks to find the difference of the values of the two variables in the system of equations:

1. y = 2x + 1
2. x + 3y = 10

We can solve this system using substitution or elimination. Let's use substitution:

1. From the first equation, we express y in terms of x: y = 2x + 1.
2. Substitute this into the second equation: x + 3(2x + 1) = 10, simplified to x + 6x + 3 = 10, which leads to 7x + 3 = 10.
3. Solve for x: 7x = 7, so x = 1.
4. Next, substitute x back into the first equation: y = 2(1) + 1, which gives us y = 3.
5. Finally, calculate the difference between the two variables: 3 (value of y) - 1 (value of x) = 2.

The difference between the values of the two variables x and y is 2.