To eliminate the x term when adding the two equations, we need to choose coefficients for each equation such that the coefficients of the x terms cancel out. Let's examine each option:
1. -10 times the first equation and 3 times the second equation:
(-10) * (2x + 3y) + (3) * (5x - 2y)
Expanding and simplifying:
-20x - 30y + 15x - 6y
-5x - 36y
The x term is not eliminated, so this choice does not work.
2. 10 times the first equation and 3 times the second equation:
(10) * (2x + 3y) + (3) * (5x - 2y)
Expanding and simplifying:
20x + 30y + 15x - 6y
35x + 24y
The x term is not eliminated, so this choice does not work.
3. -3 times the first equation and 5 times the second equation:
(-3) * (2x + 3y) + (5) * (5x - 2y)
Expanding and simplifying:
-6x - 9y + 25x - 10y
19x - 19y
The x term is not eliminated, so this choice does not work.
4. 3 times the first equation and 5 times the second equation:
(3) * (2x + 3y) + (5) * (5x - 2y)
Expanding and simplifying:
6x + 9y + 25x - 10y
31x - y
The x term is eliminated in this case, as the coefficient of x becomes zero. Therefore, the correct choice is "3 times the first equation and 5 times the second equation."