Solve the system of equations. X X A (15,5) B C E (5,-2) (5, 4) (-1,-6) (-6, -1) 2x - 3y = 16 3x + 2y = 11

Answer 1

To solve the system of equations, we can use the method of substitution or elimination.

Method of Substitution:
From the first equation, we can solve for x in terms of y:
2x - 3y = 16
2x = 3y + 16
x = (3y + 16)/2

Now we substitute this expression for x into the second equation:
3x + 2y = 11
3((3y + 16)/2) + 2y = 11
(9y + 48)/2 + 2y = 11
9y + 48 + 4y = 22
13y + 48 = 22
13y = -26
y = -2

Substitute this value of y back into the expression for x:
x = (3(-2) + 16)/2
x = (6 + 16)/2
x = 22/2
x = 11

Therefore, the solution to the system of equations is x = 11 and y = -2.

Method of Elimination:
To eliminate one of the variables, we can multiply the first equation by 2 and the second equation by 3, and then subtract the resulting equations:
2(2x - 3y) = 2(16)
3(3x + 2y) = 3(11)

4x - 6y = 32
9x + 6y = 33

By adding these equations together, the y terms will be eliminated:
4x - 6y + 9x + 6y = 32 + 33
13x = 65
x = 65/13
x = 5

Substitute this value of x back into one of the original equations, such as the first equation:
2x - 3y = 16
2(5) - 3y = 16
10 - 3y = 16
-3y = 6
y = -2

Therefore, the solution to the system of equations is x = 5 and y = -2.