Final answer:
To solve the given system of equations, substitute the second equation into the first equation. Solve the resulting quadratic equation to find the values of x. Substitute the values of x back into one of the original equations to find the corresponding y values.
Step-by-step explanation:
To solve the system of equations y = x² + 7x - 19 and y = 3x + 2 algebraically, we can substitute the second equation into the first equation:
x² + 7x - 19 = 3x + 2
Now, we can solve this quadratic equation by rearranging terms and using the quadratic formula. After finding the values of x, we can substitute them back into either of the original equations to find the corresponding y values.
For example, if we find that x = -4, we can substitute it into y = x² + 7x - 19 to get y = (-4)² + 7(-4) - 19 and solve for y.
Learn more about Solving systems of equations algebraically