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Answer 1

Answer:

Cedric system of equation has same solution as teacher solution

Step-by-step explanation:

In this question we will find the solution of the system of the teacher and then we will check that whether it satisfies the other equations or not

The system of equation of the Teacher is

8x - 16y = 14   ..............(i)

-x + 5y = -3   .................(ii)

Now taking equation (ii)

-x + 5y = -3

Subtracting 5y from both sides of the equation

-x + 5y - 5y = -3 -5y

-x = -3 - 5y

Multiplying both sides of the equation with (-1)

it becomes

x = 3 + 5y          ................(iii)

Putting this value of x in equation (i)

it becomes

8(3 + 5y) - 16y = 14

24 + 40 y -16 y = 14

24 + 24 y = 14

Subtracting 24 from both sides

24 - 24 + 24 y = 14 -24

24 y = -10

Dividing both sides by 24

$\frac{24y}{24}=\frac{-10}{24}$

$y=\frac{-5}{12}$

Putting this value in equation (iii)

x = 3 + 5$\frac{-5}{12}$

x = 3 + $\frac{-25}{12}$

Taking LCM and solving on RHS

x = $\frac{36-25}{12}$

x = $\frac{11}{12}$

Check:

Katrina system of equation:

3(x)-15(y) = 9

put value of x and y

3($\frac{11}{12}$) - 15 ($\frac{-5}{12}$) = 9

($\frac{33}{12}$) +($\frac{75}{12}$) = 9

Adding on LHS

($\frac{33+75}{12}$) = 9

($\frac{108}{12}$) = 9

9 = 9 so first equation satisfies

Second equation

8(x)-16(y) = -7

put value of x and y

8($\frac{11}{12}$) - 16 ($\frac{-5}{12}$) = -7

($\frac{88}{12}$) +($\frac{90}{12}$) = -7

Adding on LHS

($\frac{88+90}{12}$) = -7

($\frac{178}{12}$) = -7

14.83 ≠ -7 so second equation does not satisfies

So System of Katrina is not same as Teacher

Cedric system of equation:

-(x)+5(y) = -3

put value of x and y

($-\frac{11}{12}$) +5 ($\frac{-5}{12}$) = -3

($\frac{-11}{12}$) -($\frac{25}{12}$) = -3

Adding on LHS

($\frac{-11-25}{12}$) = -3

($\frac{-36}{12}$) = -3

-3 = -3 so first equation satisfies

Second equation

-4(x)+8(y) = -7

put value of x and y

-4($\frac{11}{12}$) +8 ($\frac{-5}{12}$) = -7

($\frac{-44}{12}$) -($\frac{40}{12}$) = -7

Adding on LHS

($\frac{-44-40}{12}$) = -7

($\frac{-84}{12}$) = -7

-7= -7 so second equation satisfies too

So System of Cedric is  same as Teacher