Final answer:
The system of equations 3x + 3y = 10 and -9x - 9y = -30 has an infinite number of solutions, as it represents the same line after simplification. The solution is every point on the line y = -x + 1/3.
Step-by-step explanation:
The solution of the system of equations 3x + 3y = 10 and -9x - 9y = -30 can be found by using either the substitution method, elimination method, or matrices. Here, both equations are multiples of each other, which implies that the system has an infinite number of solutions (it represents the same line). Let's solve it using the elimination method:
- First, divide the second equation by -3 to simplify it to 3x + 3y = 10.
- Then, if we add or subtract the two equations, we will end up with 0 = 0, which confirms that they are the same equation.
- Since both equations are identical after simplification, every point on the line y = -x + ⅓ is a solution to the system.
To express y in terms of x, you can rearrange the first equation to y = -x + ⅓. This is a straight line with a slope of -1 and a y-intercept of ⅓ (approximately 3.33).
Complete Question:
What is the solution of the following system
3x+3y=10
-9x-9y=-30