How do you solve the system of equations algebraically #8x-z=4, y+z=5, 11x+y=15#?

Answer 1

Madelyn Anderson

#{x=-6/7,y=111/7,z=-76/7}#

#"given :"#

#8x-z=4" "(1)#

#y+z=5" "(2)#

#x+y=15" "(3)#

#"first find (2)-(3)"#

#cancel(y)+z-x-cancel(y)=5-15#

#z-x=-10" (4)"#

#"now find (1)+(4)"#

#8x-cancel(z)+cancel(z)-x=4-10#

#8x-x=-6#

#7x=-6#

#x=-6/7#

#"use (3)"#

#-6/7+y=15#

#y=15+6/7#

#y=111/7#

#"use (2)"#

#111/7+z=5#

#z=5-111/7#

#z=(35-111)/7#

#z=-76/7#

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Answer 2

Sadie Ackerman

To solve the system of equations algebraically:

Use the second equation to express $z$ in terms of $y$ : $z = 5 - y$ .
Substitute this expression for $z$ into the first equation: $8x - (5 - y) = 4$ .
Simplify and solve for $x$ .
Substitute the values of $x$ and $z$ into the third equation to find $y$ .
Once you have $x$ , $y$ , and $z$ , you have the solution to the system.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.