How do solve the following linear system?: 7x+2y=2 , 8x+2y=3 ?

2 Answers
Narad T.
May 24, 2018

The solution is {(y=-5/2),(x=1):}

Explanation:

Solve the equations as follows

{(7x+2y=2),(8x+2y=3):}

(2)-(1), =>, {(7x+2y=2),(x=1):}

<=>, {(y=(2-7x)/2),(x=1):}

<=>, {(y=(2-7)/2),(x=1):}

<=>, {(y=-5/2),(x=1):}

Daniel L.
May 24, 2018

See explanation.

Explanation:

The original system is:

{(7x+2y=2),(8x+2y=3):}

We can easily notice that y has the same coefficient in both equations, so if we multiply any of the equations by -1 the coefficients will be opposite numbers. I multiplied the first equation and got:

{(-7x-2y=-2),(8x+2y=3):}

Now if we add both sides of the equations we get an equation with one variable only (x):

x=1

Now we have to substitute the calculated value of x to calculate y:

8+2y=3

2y=-5

y=-2.5

The solution of the system is:

{(x=1),(y=-2.5):}

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