Question

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What is the solution of the following system? {3x + 3y = 10−9x − 9y = −30

Answer 1

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

First, we multiply the second equation by -1 to make the coefficients of x in both equations match.

-1(-9x - 9y = -30)
9x + 9y = 30

Now, we add the two equations together to eliminate x.

(3x + 3y) + (9x + 9y) = (10) + (30)
12x + 12y = 40

Dividing both sides of this equation by 12, we get:

x + y = 40/12
x + y = 10/3

Now, we can substitute this value of x + y into one of the original equations to solve for another variable.

3x + 3y = 10
3x + 3(10/3) = 10
3x + 10 = 10
3x = 0
x = 0

Substituting this value back into the equation, we get:

0 + y = 10/3
y = 10/3

Therefore, the solution to the system of equations is x = 0 and y = 10/3.