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Question

The sum of the two numbers is 20. The second number is 3 times the first number. Let x = the first number and y = the second number. Write and solve the systems of equations.

There are two equations and they also ask what the x and y values are.

Answer 1

x + y =20 (x is 1st no., y is the 2nd, sum is 20)

2nd no. is 3 times the first: y = 3x

Substitute; x + 3x = 20 → 4x = 20 → x = 20/4 = 5

So 1st no. is 5, 2nd no. is 15

Answer 2

Let us change the problem into variables that we are able to use to solve the problem.

The first equation would be x + y = 20

The second equation is 3x = y

Now that we have both equations let us substitute the second equation (3x = y) into the first equation (x + y = 20)

x + 3x = 20

4x = 20

x = 5

Now that we have solved for the first variable let us substitute x to find y in any of the other equations.

3(5) = y

y = 15

∴ y = 15, x = 5