Final answer:
To solve the system of equations algebraically, you can use the method of substitution. Find the value(s) of x using factoring or the quadratic formula, then substitute it back to find the corresponding y-value(s).
Step-by-step explanation:
To solve the system of equations algebraically, we can use the method of substitution. From the second equation, we can solve for y in terms of x by rearranging the equation: y = -3x + 7. Then, substitute this expression for y in the first equation: 5x² + (-3x + 7) - 9 = 0. Simplify and solve for x by factoring or using the quadratic formula. Once you find the value(s) of x, substitute it back into one of the original equations to find the corresponding y-value(s).
Learn more about Algebraic solving of systems of equations