caciquemm
Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

The sum of two numbers is 30 and their difference is 2.  Find the two numbers by writing and solving a
system of equations

Sagot :

The numbers are 14 & 16.

The equations you need to solve are:

x + y = 30
x - y = 2  ==>  (redefine in terms of y)  y = x - 2

substitute into first equation

x + x - 2 = 30
2x = 30 + 2
x = 32/2 = 16

16 + y = 30
30 - 16 = y = 14

x = 16
y = 14

And that's how that is done.

The correct answer is:

The numbers are 14 and 16.

Explanation:

Let x and y represent the numbers. Since the sum of the numbers is 30, this gives us the equation

x+y = 30.

Since the difference of the numbers is 2, this gives us the equation

x-y = 2.

This gives us the system

[tex] \left \{ {{x+y=30} \atop {x-y=2}} \right. [/tex]

To solve this, we will eliminate one variable. Since the coefficients are all the same, but the y-variables have different signs, we will eliminate them by adding the equations together:

[tex] \left \{ {{x+y=30} \atop {+(x-y=2)}} \right.
\\
\\2x=32 [/tex]

Divide both sides by 2:

2x/2 = 32/2

x = 16.

Substitute this back into our first equation:

16+y=30

Subtract 16 from each side:

16+y-16=30-16

y=14

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.