Final answer:
To solve the equation 5x + 3y = 15 for x, we substitute the given relation y = 9 + 3x into this equation, simplify and solve for x, leading to the solution x = -6/7.
Step-by-step explanation:
To solve the equation 5x + 3y = 15 for x, we need to isolate x on one side of the equation. We are given another equation y = 9 + 3x, which allows us to substitute the value of y from the latter equation into the first one. Doing so, we get:
5x + 3(9 + 3x) = 15
Distributing the 3, we have:
5x + 27 + 9x = 15
Combining like terms, we get:
14x + 27 = 15
Subtracting 27 from both sides gives us:
14x = 15 - 27
14x = -12
Finally, dividing both sides by 14 yields:
x = -\frac{12}{14}
Reducing the fraction, we get:
x = -\frac{6}{7}
Therefore, the solution to the equation, given the constraint y = 9 + 3x, is x = -\frac{6}{7}.