How do you solve the system of equations 9x + 2y = 5 and y = 2x + 3?

To solve the system of equations algebraically, we have the following equations:

1. 9x + 2y = 5
2. y = 2x + 3

We can use substitution to solve this system. Since the second equation already expresses y in terms of x, we can substitute that expression into the first equation.

Substituting y from the second equation into the first gives us:

9x + 2(2x + 3) = 5

Now, simplify the equation:

9x + 4x + 6 = 5

Combine like terms:

13x + 6 = 5

Next, isolate x by subtracting 6 from both sides:

13x = 5 - 6

13x = -1

Now, divide by 13:

x = -\frac{1}{13}

Now that we have the value of x, we can substitute it back into the second equation to find y:

y = 2(-\frac{1}{13}) + 3

y = -\frac{2}{13} + 3

y = -\frac{2}{13} + \frac{39}{13}

y = \frac{37}{13}

So, the solution to the system of equations is:

x = -\frac{1}{13}, y = \frac{37}{13}

In conclusion, the points that satisfy both equations are (-1/13, 37/13).