crystalarnold
Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

solve system by substitution

y=3x-20

y=-x^(2)+34

Sagot :

Lilith
[tex]\begin{cases} y=3x-20 \\ y=-x^2+34 \end{cases}\\ \\ \begin{cases} y=3x-20 \\3x-20=-x^2+34 \end{cases}\\ \\\begin{cases} y=3x-20 \\x^2+3x-20-34=0 \end{cases}\\ \\\begin{cases} y=3x-20 \\x^2+3x-54=0 \end{cases}[/tex]

[tex]\begin{cases} y=3x-20 \\x^2+3x-54=0 \end{cases} \\ \\x^2+3x-54=0 \\ \\a=1, \ \ b=3, \ \ c= -54 \\ \\ \Delta =b^2 -4ac =3^2-4*1*(-54)=9+216=225 \\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{-3-\sqrt{225}}{2}=\frac{-3-15}{2}= \frac{-18}{2}=-9[/tex]

[tex]x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{-3+\sqrt{225}}{2}=\frac{-3+15}{2}= \frac{12}{2}=6[/tex]

[tex]\begin{cases} y=3x-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=3x-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=3*(-9)-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=3*6-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=-27-20 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=18-20 \\x=6 \end{cases}\\ \\ \begin{cases} y=-47 \\ x=-9 \end{cases}\ \ \vee \ \ \begin{cases} y=-2\\x=6 \end{cases}[/tex]


We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.