How do solve the following linear system?: −7x+y=−19,−2x+3y=−19?

1 Answer
Alippiun
Jan 9, 2016

x=2 and y=−5

Explanation:

For a linear system with 2 different unknowns, we use
Substitution Equation to find the actual value of the unknown.

There are two unknowns, x and y.

Firstly, let −7x+y=−19 as Equation 1
and −2x+3y=−19 as Equation 2.

From one of the equation, for example Equation 1 we can rearrange a new equation and substitute it into the other equation.

Let say, from Equation 1,
−7x+y=−19
Rearrange the equation in terms of only one unknown.
y=−19+7x as Equation 3

Substitute Equation 3 into Equation 2 and we will get;
−2x+3y=−19 given y=−19+7x,

−2x+3(−19+7x)=−19

−2x−57+21x=−19

−2x+21x=−19+57

19x=38

x=2

Substitute x=2 into Equation 3 and we will get;
y=−19+7x given x=2

y=−19+7(2)

y=−5

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