How do solve the following linear system?: x−4y=−24,x+y=−1?

1 Answer
Tony B
Jan 17, 2016

The lines cross at (x,y)→(−285,+235)→(−535,+435)

Explanation:

Given:
..x−4y=−24......................(1)
..x+y=−1..........................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider equation (2)

Take the y over to the other side of the = and change its sign

x=−1−y............................................(3)

Using equation (3) substitute for x in equation (1) giving

x−4y=−24 becomes →−1−y−4y=−24

Multiply everything by (-1) to change the signs

1+y+4y=24

1+5y=24

Move the left hand side 1 to the right and change its sign

5y=24−1 = 23

Divide both sides by 5 giving

y=235
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute y=235 in equation (2) giving:

x+y=−1 becomes →x+235=−1

Move the 235 to the other side of = and change its sign

x=−1−235 = −285

x=−285
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So the lines cross at (x,y)→(−285,235)→(−535,+435)

Tony B

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