Question

Which of the following accurately shows the first step when solving the following system of equations by substitution? f (x) = -5x^{2} + 2x + 7 g (x) = -3x + 4

Answer 1

`-5x^2+2x+7=-3x+4`

Explanation:

`f(x)=-5x^2+2x+7`

`g(x)=-3x+4`

To solve the system of equations, equate the equations:

`\begin{aligned} f(x) &=g(x)\\\implies -5x^2+2x+7&=-3x+4\\-5x^2+2x+7+3x-4 & =0\\-5x^2+5x+3 & =0\\5x^2-5x-3 & =0\end{aligned}`

Use the quadratic formula to solve for x

Quadratic Formula

`x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when}\:ax^2+bx+c=0`

`\implies x=(-(-5) \pm √((-5)^2-4(5)(-3)) )/(2(5))`

`\implies x=(5 \pm √(85))/(10)`