algebra 1 system of equations

Question

the sum of two numbers is 365 and the difference is 111. help me find the system of equations to represent the situation then solve it to find both numbers

Answer 1

Let x = the first number and y = the second number.

First equation:

“The sum of two numbers is 365”

The sum means to add. So:

x + y =365

Second equation:

”the difference is 111”

The difference means subtract. So:

x - y = 111

If we put both equations together, we have:

x + y = 365

x - y = 111

There are several ways to solve a system of equation: Graphing, Substitution, and Elimination. All three methods work all of the time, however, you want to use the method that will make the problem easiest to solve. If we look at these two equations together, we notice that the x’s and the y’s have the same respective coefficients, that being 1. But since the y’s have different signs, we can add the equations together without any extra manipulation and eliminate the y’s, thus being left with one variable.

Add the equations:

2x = 476

Divide by 2 on both sides:

x = 238

So one of the numbers we are solving for is 238.

Plug that x back in to either equation and solve for y. The first equation will be just slightly easier this time since everything is positive.

x + y = 365

238 + y = 365

Subtract 238 from both sides:

y = 127

Check our work:

The sum of both numbers is 365 (x + y = 365): 238 + 127 does equal 365.

The difference of both numbers is 111 (x - y = 111): 238 - 127 does equal 111.

Answer 2

The system is

n + m = 365

n - m = 111

Add the two equations and get

2n = 476

and solve for n. Then plug the value of n into either equation of the system and solve for m.