Two times a number plus three times another number equals four. Three times the first number plus four times the other number is seven. Find the numbers.

2x + 3y = 4

3x + 4y =7

from top equation:  2x =4 - 3y   so   x= 2- 3y/2

substitute for x into bottom equation:

3(2- 3y/2) + 4y =7

solve for y:

6 - 9y/2 + 4y=7

4y -4.5y = 1

-.5y=1

y= - 2

x= 2- 3(-2)/2 = 2+3=5

solution is x = 5 and y = -2

Check:

2x + 3y = 4

2(5) + 3(-2) = 4

10 -6=4

4=4

and

3x + 4y =7

3(5) + 4(-2)=7

15 -8=7

7=7