The sum of two numbers is 16 and their difference is 6 what is the answer?

Question

The sum of two numbers is 16 and their difference is 6 what is the answer?

Answer 1

11 and 5

x+y = 16

x-y=6

add them to get

2x = 22

x = 11

y = 5

You could also solve this by trial and error.

two numbers sum to 16. That could be 15+1, 14+2, 13+3, 12+4, 11+5

keep going until you get a pair that have a difference of 6

15-1=14, 14-2 = 12, 13=3= 10, 12-4 = 8, 11-5 = 6 so the two numbers are 11 and 5

or make 2 equations out of the information.

Let x= one number, and y= the other number

they sum to 16

x+y = 16

their difference is 6

x-y = 6. It really doesn't matter if you make it x-y=6 or y-x=6, either way you'll end up with 11 and 5 as the two numbers

x+y = 16

x-y= 6 If you have 2 equations 2 unknowns you can solve for both variables. Here by addition

x+y = 16

x-y = 6

2x = 22

divide by 2

x = 11

then plug that value of x into either of the original 2 equations. Plug into both as a check on the answer

11+y = 16

y = 16-11 = 5

x-y = 6

11-5 = 6

another way to solve the 2 equations is graph them, carefully plot the 2 lines and find their intersection

plot a few points for each, connect the points to make 2 straight lines, you can at least estimate fairly closely where they intersect

x+y = 16 is the same as y =-x +16 which has slope -1, that's downward sloping at a -45 degree angle with the x axis and a y intercept of 16. Plot 2 points (0,16) and (0,16) the y and x intercept. Connect them with a straight line.

x-y= 6 is equivalent to y = x-6, a line with slope +1 and y intercept -6

y intercept is the point (0,-6), x intercept is when y=0, (6,0) plot those 2 points, connect them with a straight line. The extend the last line up to the right until it intersects the first line. Use graph paper, or just a rough sketch and you'll see the point of intersection is (11,5), which means the two numbers are 11 and 5