Question

{2x+3y=11
{3x+3y=18

What is the solution to the above system of equations?

Answer 1

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

We can multiply the first equation by 3 to make the coefficients of y in both equations the same:
(3)(2x+3y)= (3)(11)
6x + 9y = 33

Now we can subtract the second equation from the first equation:
(6x + 9y) - (3x + 3y) = 33 - 18
3x + 6y = 15

Next, we can divide both sides of this equation by 3 to isolate x:
(3x + 6y)/3 = 15/3
x + 2y = 5

Now we can solve this equation for x:
x = 5 - 2y

We can substitute this value of x into one of the original equations, let's choose the first one:
2(5 - 2y) + 3y = 11
10 - 4y + 3y = 11
-y = 1
y = -1

Now substitute this value of y back into the equation x = 5 - 2y:
x = 5 - 2(-1)
x = 5 + 2
x = 7

Therefore, the solution to the system of equations is x = 7 and y = -1.