Question

Three students each examine the system of linear equations shown.

8x+4y=16
8x+2y=8
Caleb says there is exactly one solution. Jeremy says there is no solution. Kim says there are infinitely many solutions.

Answer 1

The solution is (0, 4), and there is only one solution

Explanation:

Let's actually solve the system if that's possible. Solving the second equation for 8x, we get 8x = 8 - 2y. Substituting this result into the first equation eliminates y:

8 - 2y + 4y = 16,

which simplifies to 2y = 8 and then y = 4.

Substituting 4 for y in the second equation yields 8x + 2(4) = 8, so we can quickly deduce that x = 0.

The solution is (0, 4), and there is only one solution

Answer 2

Caleb is right because there is exactly one solution at (0, 4).
Linear equation
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Given the equation:
8x + 4y = 16 (1)
8x + 2y = 8 (2)
Solving equation 1 and 2 simultaneously gives:
x = 0, y = 4
Caleb is right because there is exactly one solution at (0, 4).