If 2x + 3y = 17 and 3x + 4y = 24, then 5x +7y
a) 7
b) 41
c) 3
d) -7
e) -41

The answer is B) 41
Step 1: Find x and y
Step 2: Calculate 5x + 7y

Step 1.
2x + 3y = 17
3x + 4y = 24

Multiple the first equation by 3, and the second one by -2:
3 * 2x + 3 * 3y = 3 * 17
(-2) * 3x + (-2) * 4y = (-2) * 24

6x + 9y = 51
-6x - 8y = - 48

Sum up these two equations:
6x + 9y + (-6x - 8y) = 51 + (-48)
6x + 9y - 6x - 8y = 51 - 48

6x can be canceled:
9y - 8y = 3
y = 3

Now, replace y in one of the equtions:
3x + 4y = 24
3x + 4*3 = 24
3x + 12 = 24
3x = 24 - 12
3x = 12
x = 12/3 = 4

Step 2:
Now that we know that x = 4 and y = 3, we can calculate 5x +7y:
5x + 7y = 5 * 4 + 7 * 3 = 20 + 21 = 41