Final answer:
To solve the system of linear equations, we can use the method of substitution or elimination. The solution to the system of linear equations is a = 20/3, b = -15, and c = 1.
Step-by-step explanation:
To solve the system of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution:
Since we know that 3c = 3, we can solve for c by dividing both sides of the equation by 3, which gives us c = 1.
Substituting the value of c into the first equation, we have 2a + 2b + 1 = -9. Rearranging the terms, we get 2a + 2b = -10.
Substituting the value of c into the second equation, we have 5a + 2b - 3(1) = 7.
Simplifying, we get 5a + 2b = 10.
Now we have a system of two equations:
2a + 2b = -10
5a + 2b = 10
We can subtract the first equation from the second equation to eliminate b:
5a + 2b - (2a + 2b) = 10 - (-10)
3a = 20
Dividing both sides of the equation by 3, we get a = 20/3. Therefore, the solution to the system of linear equations is a = 20/3, b = -15, and c = 1.
Learn more about Solving Systems of Linear Equations