Question

Find the solution to the following system by substitution.

4x + y = 40
y = 4x
OA. (0,40)
OB. (5,20)
O C. (10,40)
D. (10,0)

Answer 1

B. (5, 20)

Explanation:

You want to use substitution to find the solution to this system of equations:

• 4x +y = 40
• y = 4x

Substitution

We are given an expression for y, so we can use that to substitute in the first equation:

4x +4x = 40 . . . . . . substitute 4x for y

8x = 40 . . . . . . . . . . collect terms

x = 40/8 = 5 . . . . . . divide by 8

Then ...

y = 4x = 4(5) = 20 . . . . . use the second equation to find y

The solution is (x, y) = (5, 20), matching choice B.

Alternate solution

We are also given an expression for 4x, so we can substitute that into the first equation:

y +y = 40 . . . . . . . . . substitute y for 4x

2y = 40 . . . . . . . . . . collect terms

y = 40/2 = 20 . . . . . divide by 2

20 = 4x . . . . . . . . . use the 2nd equation to find x

x = 20/4 = 5 . . . . . divide by 4

The solution is (x, y) = (5, 20), matching choice B.

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