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

Answer 1

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

Using the method of substitution:
1) Solve one equation for one variable in terms of the other.
From the first equation, we have:
3x + 3y = 10
Rearranging, we get:
3y = 10 - 3x
y = (10 - 3x)/3

2) Substitute the expression for the variable into the other equation.
Substituting y in the second equation, we get:
-9x - 9((10 - 3x)/3) = -30

3) Simplify and solve for x.
Multiplying through by 3 to eliminate the fraction, we have:
-27x - 90 + 27x = -90
Simplifying, we get:
-90 = -90
This equation is true for all values of x. There is no unique value for x.

4) Solve for y using the expression obtained in step 1.
Using the expression for y from step 1:
y = (10 - 3x)/3
Substituting any value of x, we get a corresponding value of y.

Therefore, the solution to the system of equations is:
(x, y) = (x, (10 - 3x)/3)