dhontes512
Answered

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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

Which Of The Following Accurately Shows The First Step When Solving The Following System Of Equations By Substitution F X 5x2 2x 7 G X 3x 4 class=

Sagot :

semsee45

Answer:

[tex]-5x^2+2x+7=-3x+4[/tex]

Step-by-step explanation:

[tex]f(x)=-5x^2+2x+7[/tex]

[tex]g(x)=-3x+4[/tex]

To solve the system of equations, equate the equations:

[tex]\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}[/tex]

Use the quadratic formula to solve for x

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\implies x=\dfrac{-(-5) \pm \sqrt{(-5)^2-4(5)(-3)} }{2(5)}[/tex]

[tex]\implies x=\dfrac{5 \pm \sqrt{85}}{10}[/tex]

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