Jack wants to find the solution to a system of equations using y = x + 3 and y = x^2 + 6x - 21. Betty says that Jack can solve x^2 + 5x - 24 = 0 to find the x-coordinates of the solutions of the system. Explain and demonstrate why Betty is correct.

Question

anonymous · Answer

y = x + 3
y = x^2 + 6x - 21

When you combine them you get:
x + 3 = y = x^2 + 6x - 21
x + 3 = x^2 + 6x - 21

Subtract x +3 from both sides:
0 = x^2 + 5x - 24

anonymous · Answer

To solve y = x + 3 simultaneously with y = x^2 + 6x - 21, we put them equal to each other to get 
x^2 + 6x - 21 = x + 3. 
Putting all the terms on the left gives x^2 + 6x - 21 - x - 3 = 0 which gives x^2 + 5x - 24 = 0. 
Betty is correct!