Question 283529
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:

{{{x + y = 7}}}
I have y by itself, by subtracting the x to the other side:
{{{y = -x + 7}}}

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

{{{2x + 3y = 13}}}

{{{2x + 3(-x + 7) = 13}}}

Follow order of operations:

{{{2x + (-3x) + 21 = 13}}}
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:
{{{2x - 3x + 21 = 13}}}

Next you subtract the like terms= x's :

{{{-x + 21 = 13}}}

To get x by itself, subtract the 21 :

{{{-x = -21 + 13}}}
{{{-x = -8}}}

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:

{{{-x/-1 = -8/-1}}}
Negative/Negative equals Positive
{{{x = 8}}}  

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

{{{x + y = 7}}}
{{{8 + y = 7}}}

Get y by itself:

{{{y = -8 + 7}}}
{{{y = -1}}}

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

{{{2x + 3y = 13}}}
{{{2(8) + 3(-1) = 13}}}

{{{16 - 3 = 13}}}

{{{13 = 13}}} Checks out.