Mathematics: Solve the system of equations y=2x-3 y=x^2-2x-8

It s basically just multiplying. 9*4= 36 . so 36 different options. ...

Solve the system of equations y=2x-3 y=x^2-2x-8

Ответ:

10040816

10.03.2022

Mathematics

$\boxed{x = -1; \, x = 5}$

Step-by-step explanation:

(a) Set the two functions equal to each other

$\begin{array}{rcl}y & = & 2x - 3\\y & = & x^{2} - 2x - 8\\2x - 3 & = & x^{2} - 2x - 8\\2x & = & x^{2} -2x - 5\\x^{2} - 4x - 5 & = & 0\\\end{array}$

(b) Factor the quadratic equation

Find two numbers that multiply to give -5 and add to give ₄9.

Possible pairs are 1, -5; -1, 5;

By trial and error, you will find that 1 and -5 work:

1 × (-5) = -5 and 1 - 5= -4

x² - 4x - 8 = (x + 1)(x - 5)

$\begin{array}{rlcrl}x+ 1 & =0 & \qquad & x - 5 & =0\\x & = -1 & \qquad & x & = 5\\\end{array}\\\text{The solution to the system of equations is }\boxed{\mathbf{x = -1; x = 5}}$

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Solve the system of equations y=2x-3 y=x^2-2x-8

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