Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Use substitution to solve the following system of equations.
d + e - f = -3
e = f + d + 7
f = 2e - 6

a. d = 3, e = -4, f = 2
b. d = -4, e = 3, f = 2
c. d = -2, e = 4, f = -5
d. d = -5, e = 4, f = 2

Sagot :

naǫ
[tex]d+e-f=-3 \\ e=f+d+7 \\ f=2e-6 \\ \\ \hbox{substitute 2e-6 for f in the 2nd equation and solve for e:} \\ e=2e-6+d+7 \\ e=2e+d+1 \ \ \ |-2e \\ -e=d+1 \ \ \ |\times (-1) \\ e=-d-1 \\ \\ \hbox{substitute -d-1 for e in the 3rd equation and solve for f:} \\ f=2(-d-1)-6 \\ f=-2d-2-6 \\ f=-2d-8[/tex]

[tex]\hbox{substitute -d-1 for e and -2d-8 for f in the 1st equation and solve for d:} \\ d+(-d-1)-(-2d-8)=-3 \\ d-d-1+2d+8=-3 \\ 2d+7=-3 \ \ \ |-7 \\ 2d=-10 \ \ \ |\div 2 \\ d=-5 \\ \\ e=-d-1=-(-5)-1=5-1=4 \\ \\ f=-2d-8=-2 \times (-5)-8=10-8=2 \\ \\ \boxed{d=-5} \\ \boxed{e=4} \\ \boxed{f=2} \\ \hbox{answer D}[/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.