find the solution by the addition method check your answer?

Question

2x + y =4
3x - 2y = -1

Answer 1

2x + y =4
3x - 2y = -1

4x + 2y = 8
3x - 2y = -1

7x = 7
2x + y = 4

x = 1
y = 2

Answer 2

*Solve for "x" or "y" and eliminate a variable: let's solve for "x" and eliminate "y"

First: take the second coefficient from the top equation (1) and multiply it by the second equation. Take the second coefficient
from the second equation (-2) and multiply it by the first equation. Since one coefficient (-2) is negative, it has to be positive to eliminate "y"

2(2x + 1y = 4)
1(3x - 2y = -1)
--------------------
4x + 2y = 8
+ 3x - 2y = - 1
--------------------
7x = 7
7x/7 = 7/7
x = 1

Second: solve for "y" and eliminate "x" > take the first coefficient
from the first equation (2) and multiply it by the second equation. take the first coefficient from the second equation (3) and multiply it by the first equation. Since both coefficients are positive, one has to be negative> let's make 3 negative:

-3(2x + 1y = 4)
2(3x - 2y = -1)
------------------
- 6x - 3y = -12
+ 6x - 4y = - 2
---------------------
-7y = -14
-7y/-7 = -14/-7
y = 2

(1, 2)