X and y have a sum of 20. The value of y is four times as big as the value of x

Question

I need to find the value of x and y

Answer 1

Hi Lizzie,

If we are given the sum of x and y is 20, we can express this statement using

the following equation:

x + y = 20

If we are also given the value of y is four times as big as the value of x, we can

express this statement with the following equation:

y = 4x

We can now use the system of equations below to determine the value of x and y.

(Step 1) We are substituting 4x for the variable y in the second equation.

x + y = 20

x + 4x = 20

(Step 2) We are adding like terms in the second equation.

x + y = 20

5x = 20

(Step 3) Solve for y by multiplying the second equation by -1/5.

x + y = 20

(-1/5)5x = 20(-1/5)

(Step 4) Solve the system of equations for y.

x + y = 20

-x = -4

y = 16

(Step 5) Substitute our value of y into the first equation and solve for x.

x + 16 = 20

x = 20 - 16

x = 4

(Answer)

The value of x is 4. The value of y is 16.