Question

i) 49 + 51y = 499
51x + 49y = 501
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رم​

Answer 1

Question:-

49x + 51y = 499

51x + 49y = 501

Solution:-

49x + 51y = 499.........(i)

51x + 49y = 501.........(ii)

Solving the following pair of linear simultaneous equations by the elimination method.

49x + 51y = 499 } ×51

=> 2499x + 2601y = 25449........(iii)

51x + 49y = 501 } ×49

=> 2499x + 2401y = 24549........(iv)

Subtracting eqn. (i) & (ii), we get:-

2499x + 2601y = 25449

2499x + 2401y = 24549

- - -

___________________________

200y = 900

y = 900/200

y = 4.5

Now, Putting the value of y in eqn.(i), we get:-

49x + 51y = 499

=> 49x + 51×4.5 = 499

=> 49x + 229.5 = 499

=> 49x = 499 - 229.5

=> 49x = 269.5

=> x = 269.5/49

=> x = 5.5

Hence, The value of x is 5.5 and the value of y is 4.5 respectively.

Answer 2

Answer:

$49+51y=499,\:51x+49y=501\quad :\quad x=\dfrac{389}{289},\:y=\dfrac{150}{17}$

Step-by-step explanation:

$\begin{bmatrix}49+51y=499\\ 51x+49y=501\end{bmatrix}$

$\mathrm{Isolate}\:y\:\mathrm{for}\:49+51y=499$

$49+51y=499$

$\mathrm{Subtract\:}49\mathrm{\:from\:both\:sides}$

$49+51y-49=499-49$

$\mathrm{Simplify}$

$51y=450$

$\mathrm{Divide\:both\:sides\:by\:}51$

$\dfrac{51y}{51}=\dfrac{450}{51}$

$\mathrm{Simplify}$

$y=\dfrac{150}{17}$

$\mathrm{Subsititute\:}y=\dfrac{150}{17}$

$\begin{bmatrix}51x+49\cdot \dfrac{150}{17}=501\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:51x+49\dfrac{150}{17}=501$

$51x+49\cdot \dfrac{150}{17}=501$

$\mathrm{Subtract\:}49\dfrac{150}{17}\mathrm{\:from\:both\:sides}$

$51x+49\cdot \dfrac{150}{17}-49\cdot \dfrac{150}{17}=501-49\cdot \dfrac{150}{17}$

$\mathrm{Simplify}$

$51x=\dfrac{1167}{17}$

$\mathrm{Divide\:both\:sides\:by\:}51$

$\dfrac{51x}{51}=\dfrac{\dfrac{1167}{17}}{51}$

$\mathrm{Simplify}$

$x=\dfrac{389}{289}$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$x=\dfrac{389}{289},\:y=\dfrac{150}{17}$