If x+y = 6 and x-y =4, what is the value of 2x + 3y? a) 9 b) 10 c)11 d) 12 e) 13?

lets call "x+y=6" equation 1, and the "x-y=4" equation 2.
equation1 + equation2:
x+x+y-y=10
2x=10
x=5

in equation 1, we substitute x for 5:
5+y=6
y=1

Back to the original question 2x+3y?
x=5 and y=1 so it can be written as (2*5) + (3*1)
which gives us 10+3=13
so it is E

x + y = 6
x- y = 4

Let's rearrange and solve for x and y.

x = 6 - y

x - y = 4
(6 - y) - y = 4
6 - 2y = 4
2 = 2y
1 = y

x = 6 - (1)
x = 5

Therefore x = 5 and y = 1. Now let's substitute those values into the third equation:

2x + 3y
2(5) + 3(1)
10 + 3
13

Thus, the solution is e) 13.

Hope this helps!

Given:
x+y = 6
x-y =4 <<<add the equations to eliminate y
2x = 10
x = 5

x+y = 6 <<<original equation
x=5
5 +y = 6
y=1

so 2x + 3y = ?
2(5) + 3(1) = 10+3
= 13
Answer E.

2x = 10
x = 5
y = 1

2x + 3y = 10 + 3 = 13_____Option e)

its 13, because for the two equations to work, x=5 and y=1. 5+1=6 and 5-1=4