Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Solve each system using substitution or elimination. Show all required work. -10x^2+80x+y=155 5x^2-40x+y=-85

Sagot :

Answer:

[tex]x = 4[/tex]

[tex]y = -5[/tex]

Step-by-step explanation:

Given

[tex]-10x^2+80x+y=155[/tex]

[tex]5x^2-40x+y=-85[/tex]

Required

Solve by substitution

Make y the subject in [tex]5x^2-40x+y=-85[/tex]

[tex]5x^2-40x+y=-85[/tex]

[tex]y = -5x^2 + 40x - 85[/tex]

Substitute [tex]y = -5x^2 + 40x - 85[/tex] in the first equation

[tex]-10x^2+80x+y=155[/tex]

[tex]-10x^2 + 80x -5x^2 + 40x - 85 = 155[/tex]

Collect Like Terms

[tex]-5x^2-10x^2 + 80x + 40x - 85 - 155=0[/tex]

[tex]-15x^2 + 120x-240=0[/tex]

Divide through by -15

[tex]x^2 -8x + 16 = 0[/tex]

[tex]x^2 - 4x - 4x + 16 = 0[/tex]

[tex]x(x - 4) - 4(x - 4) = 0[/tex]

[tex](x - 4)(x - 4) = 0[/tex]

[tex]x - 4\ = 0[/tex] or [tex]x - 4\ = 0[/tex]

[tex]x = 4[/tex] or [tex]x = 4[/tex]

[tex]x = 4[/tex]

Substitute 4 for x in [tex]y = -5x^2 + 40x - 85[/tex]

[tex]y = -5(4)^2 + 40 * 4 - 85[/tex]

[tex]y = -5*16 + 40 * 4 - 85[/tex]

[tex]y = -80 + 160 - 85[/tex]

[tex]y = -5[/tex]

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.