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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.

Three students each examine the system of linear equations shown 8x4y16 8x2y8 Caleb says there is exactly one solution Jeremy says there is no solution Kim says class=

Respuesta :

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).
altavistard

Answer:

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

Step-by-step 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

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