Answer: To find the solution of the system of equations:
y = 3x^2 + 5x + 4
y = 2x + 10
We set the two expressions for y equal to each other:
3x^2 + 5x + 4 = 2x + 10
Subtracting 2x and 10 from both sides:
3x^2 + 5x - 2x + 4 - 10 = 0
3x^2 + 3x - 6 = 0
We can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 3, b = 3, and c = -6. Plugging these values into the formula:
x = (-3 ± √(3^2 - 4 * 3 * -6)) / 2 * 3
x = (-3 ± √(9 + 72)) / 6
x = (-3 ± √(81)) / 6
x = (-3 ± 9) / 6
x = (-3 + 9) / 6 or (-3 - 9) / 6
x = 6 / 6 or -12 / 6
x = 1 or -2
So the solution of the system of equations is (1, 17) or (-2, 4).
Explanation: