Final answer:
To solve the given system of equations, we rearranged one equation to solve for y and substituted it into the other equation. This resulted in solving for x first, and then using that value to find y. The final solution is x = -16 / 13 and y = 72 / 13.
Step-by-step explanation:
To solve the system of equations 3x - 5y = 9 and 5x = -4y + 4 for x and y, we can use the substitution or elimination method. In this case, let's use substitution. The second equation can be rearranged to isolate y, giving us y = (5x - 4) / -4. Substituting this expression into the first equation yields 3x - 5((5x - 4) / -4) = 9. Multiplying both sides of the equation by -4 to clear the fraction, we get -12x + 25x - 20 = -36, which simplifies to 13x - 20 = -36. Adding 20 to both sides gives us 13x = -16, and finally, dividing by 13 yields x = -16 / 13.
Now, we can substitute x back into the rearranged second equation: y = (5(-16 / 13) - 4) / -4, which simplifies to y = (-80 / 13 - 4) / -4. Multiplying the numerator by the reciprocal of the denominator gives us y = (80 / 13 + 4) / 4, which further simplifies to y = 20 / 13 + 4. Simplifying this expression gives us the value for y: y = 72 / 13.