Question

2x - 3y = 16

3x + 2y = 11

solve the system of equations

Answer 1

To solve the system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method:

First, let's eliminate the y variable by multiplying the first equation by 2 and the second equation by 3:

(2) * (2x - 3y) = (2) * 16
4x - 6y = 32

(3) * (3x + 2y) = (3) * 11
9x + 6y = 33

Now, we can add the two new equations together:

(4x - 6y) + (9x + 6y) = 32 + 33
13x = 65

Divide both sides of the equation by 13 to isolate x:

13x/13 = 65/13
x = 5

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's substitute x = 5 into the first equation:

2(5) - 3y = 16
10 - 3y = 16

Subtract 10 from both sides of the equation:

-3y = 16 - 10
-3y = 6

Now, divide both sides of the equation by -3 to isolate y:

-3y/-3 = 6/-3
y = -2

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