Answer:
(x, y) = (-1/2, 5/2)
Explanation:
To solve this system of equations using substitution, we can use the first equation to express y in terms of x, and then substitute that expression into the second equation to get an equation in terms of x alone.
Starting with the first equation, we have:
y = x + 3
We can now substitute this expression for y into the second equation:
3x + 3y = 6
3x + 3(x + 3) = 6
Simplifying the right-hand side:
3x + 3x + 9 = 6
6x = -3
x = -1/2
Now that we have solved for x, we can substitute this value back into the first equation to find y:
y = x + 3
y = -1/2 + 3
y = 5/2
Therefore, the solution to the system of equations is (x, y) = (-1/2, 5/2).
To check our solution, we can substitute these values back into both equations and verify that they hold true:
y = x + 3
5/2 = -1/2 + 3
5/2 = 5/2
This equation holds true, so the first equation is satisfied by our solution.
3x + 3y = 6
3(-1/2) + 3(5/2) = 6
-3/2 + 15/2 = 6
6 = 6
This equation also holds true, so the second equation is satisfied by our solution as well.
Therefore, we can conclude that our solution is correct.
The equations have two variables, x and y, and we can use substitution to solve for one variable in terms of the other. By substituting the expression for y into the second equation and solving for x, we get the value of x as -1/2. We can then substitute this value back into the first equation to get the value of y, which is 5/2. This means that the solution to the system of equations is (x, y) = (-1/2, 5/2) and we can check that this solution satisfies both equations.
Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]