Question

How many solutions does the following system have? Choose the explanation that best fits your answer. y=−12x+4,4x+8y=16

Answer 1

There will be only one solution because the slope and the y-intercept are different meaning that they are not be parrell or will on top of one another.

Answer 2

Equation 1)  y = -12x + 4
Equation 2)  4x + 8y = 16

To find out how many solutions something has, you have to solve it first.

So, rearrange equation 1 so that x and y are on the same side. To do so, you add 12x to both sides.

1)  12x + y = 4
2)  4x + 8y = 16

Multiply all of equation 2 by 3.

2)  3(4x + 8y = 16)

Simplify.

2)  12x + 24y = 48
1)  12x + y = 4

Subtract equations from each other.

23y = 44

y = 44/23 OR 1 19/23

Because y has a solution, x does as well.

Because we know that, we do NOT have to solve the whole equation.

So, this set of equations has 1 solution.

~Hope I helped!~