Answered

Find solutions to your problems with the help of IDNLearn.com's knowledgeable users. Our community provides timely and precise responses to help you understand and solve any issue you face.

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 :

Naǫidn
[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]
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.