Final answer:
To solve the system of equations y=x²-3x and y=x+5, set them equal and simplify to get x² - 4x - 5 = 0. Factoring yields (x - 5)(x + 1) = 0, giving us x values of 5 and -1, and corresponding y values of 10 and 4, resulting in two solutions: (5, 10) and (-1, 4).
Step-by-step explanation:
To solve the system of equations y=x²-3x and y=x+5, we will set the two equations equal to each other becausethey both equal y. So, x² - 3x = x + 5.
Next, we will rearrange the equation to bring all terms to one side. This yields x² - 3x - x - 5 = 0, or simplifying, x² - 4x - 5 = 0.
Now we will factor the quadratic equation if possible or use the quadratic formula to solve for x. Factoring gives us (x - 5)(x + 1) = 0. Therefore, the solutions for x are 5 and -1.
Finally, we'll substitute these values back into either original equation to find the corresponding y values. For x = 5, y = 5 + 5 = 10, and for x = -1, y = -1 + 5 = 4. Hence, we have two solutions for the system of equations: (5, 10) and (-1, 4).