How do solve the following linear system?: x−2y=−3,2x−5y=3?

1 Answer
smendyka
Mar 17, 2017

See the entire solution process below:

Explanation:

Step 1) Solve the first equation for x:

x−2y=−3

x−2y+2y=−3+2y

x−0=−3+2y

x=−3+2y

Step 2) Substitute −3+2y for x in the second equation and solve for y:

2x−5y=3 becomes:

2(−3+2y)−5y=3

(2×−3)+(2×2y)−5y=3

−6+4y−5y=3

−6+(4−5)y=3

−6−y=3

6−6−y=6+3

0−y=9

−y=9

−1×−y=−1×9

y=−9

Step 3) Substitute −9 for y in the solution to the first equation at the end of Step 1 and calculate x:

x=−3+2y becomes:

x=−3+(2×−9)

x=−3−18

x=−21

The solution is: x=−21 and y=−9 or (−21,−9)

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