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How do you solve this system of equations #7x + 8y = - 10; - x + y = - 20#?

Answer 1

Eva Adamson

See a solution process below:

Step 1) Solve the second equation for #y#:

#-x + y = -20#

#color(red)(x) - x + y = color(red)(x) - 20#

#0 + y = x - 20#

#y = x - 20#

Step 2) Substitute #(x - 20)# for #y# in the first equation and solve for #x#:

#7x + 8y = -10# becomes:

#7x + 8(x - 20) = -10#

#7x + (8 xx x) - (8 xx 20) = -10#

#7x + 8x - 160 = -10#

#(7 + 8)x - 160 = -10#

#15x - 160 = -10#

#15x - 160 + color(red)(160) = -10 + color(red)(160)#

#15x - 0 = 150#

#15x = 150#

#(15x)/color(red)(15) = 150/color(red)(15)#

#(color(red)(cancel(color(black)(15)))x)/cancel(color(red)(15)) = 10#

#x = 10#

Step 2) Substitute #10# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:

#y = x - 20# becomes:

#y = 10 - 20#

#y = -10#

The Solution Is:* #x = 10# and #y = -10# or #(10, -10)#

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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.