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What is the solution of the system defined by y = -x + 5 and 5x + 2y = 14?

A. x = 1/3 , y = 11/7

B. x = 4/3 , y = 11/3

C. x = 5/11 , y= 0

D. x= 4/3 , y=1

Answer :

Petroniusz
 1 way The method of opposite coefficients
We multiply equally so that one of the variables was expressed opposite numbers . I chose y

y = -x + 5   [ *(-2)
5x + 2y = 14

-2y - 2x =  - 10
 2y + 5x=   14
------------------------- add the equation
3x = 4   ⇔   x = 4/3

We substitute the value of x to the equation. We can choose any
y = -x + 5 = - 4/3 + 5 = 15/3 - 4/3 = 11/3

Answer B
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2 way
method of substitution

 y = -x + 5         y value we put into the second equation
5x + 2y = 14

y = -x +5
5x +2*(-x + 5) = 14

y = -x + 5
5x - 2x + 10 = 14

y = -x + 5
3x = 14 - 10

y  = -x + 5
3x = 4  [:3

y = -x + 5
x = 4/3   we can put an x value of the first equation

y = -x + 5 = - 4/3 + 5 = 15/3 - 4/3 = 11/3

Answer B

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