Question

Two equations are given below:

m + 5n = 20
m = n − 4

What is the solution to the set of equations in the form (m, n)?

(3, 7)
(0, 4)
(5, 1)
(2, 6)

Answer 1

(0,4)

Explanation:

Because the problem gives you the value of what m would equal in terms of n you would substitute n - 4 for m in the equation above, resulting in:

n - 4 + 5n = 20

6n - 4 = 20

6n = 24

n = 4

Now that you know n = 4, you already can see that the answer would be (0,4), however to check you can substitute 4 for n into the second equation.

m = 4 - 4

m = 0

Because this results in m = 0, that tells you that (0,4) is the right answer.

Answer 2

(0, 4)

Explanation:

So you can solve the equation by substitution. The solution of a systems of equations, is when they both intersect, or when the (x, y) values are exactly equal, which is why I can substitute the m of the second equation into the first equation, because I'm looking for when they're equal, and that is when m is going to be equal in both equations, as well as the n value.

original equation:

m + 5n = 20

substitute n-4 as m in the equation

(n-4) + 5n = 20

simplify:

6n-4 = 20

add 4 to both equations

6n = 24

divide both sides by 6

n = 4

Now to find m, simply substitute 4 as n in either equation:

Original equation:

m = n - 4

substitute 4 as n

m = 4-4

m=0

so m=0, and n=4, so the solution in the form (m, n) = (0, 4)