SOLUTION: two times a number plus three times another number equals 13. the sum of the two numbers is 7

Question 283529: two times a number plus three times another number equals 13. the sum of the two numbers is 7
Answer by JenniferTutors(83) (Show Source): You can put this solution on YOUR website!
Two times a number: 2x
x = (unknown)a number
Two times a number plus three times another number: 2x + 3y
y = (unknown) another number
Two times a number plus three times another number equals 13:
2x + 3y = 13
the sum of the two numbers is 7
"is" usually can refer to equals
the 2 unknown numbers are x & y, so:
x + y = 17
Now you have two equations: 2x + 3y = 13 & x + y = 7
Here you can see that if you get one variable by itself in the second equation, you can place it into the first equation:

I have y by itself, by subtracting the x to the other side:

Next, you can place the y into the first equation:

Follow order of operations:

I don't usually like to keep my problems like this, math books usually show you this way, honestly I think it's confusing, as long as you remember to keep the negative to the 3, look below I'll rewrite it so there isn't as many positive & neg signs:

Next you subtract the like terms= x's :

To get x by itself, subtract the 21 :

You cannot leave variables in the negative this way, since a variable 'x'
always has a one, but we usually don't write it '1x', Well to make the x positive we need to divide a negative 1 to both sides of the equation:

Negative/Negative equals Positive

Now you can place the x value into the second equation:

Get y by itself:

Now you have both of the values, x = 8, y = -1
To Check, place the values into the first equation:

Checks out.

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