Question

Solve the following simultaneous lin.
1 (1) 2x - 3/4=3
5x-2y=7​

Answer 1

Answer:

x = 15/8 and y = 19/16

Step-by-step explanation:

According to the given question,

• 2x-3/4 = 3 ----------1)

• 5x - 2y = 7 --------2)

From 1st equation we get,

• 2x - 3/4 = 3

• 2x = 3/4 + 3

• 2x = 15/4

• x = 15/8

Now, putting the value of x in 2nd equation we get,

• 5x-2y = 7

• 5×15/8 - 2y = 7

• 5×15/8 - 7 = 2y

• 75/8 - 7 = 2y

• 75-56/8 = 2y

• 19/8 = 2y

• 2y = 19/8

• y = 19/16

Thus value of x = 15/8 and y = 19/16 respectively.

Answer 2

Answer:

$2x-\dfrac{3}{4}=3,\:5x-2y=7\quad :\quad y=\dfrac{19}{16},\:x=\dfrac{15}{8}$

Step-by-step explanation:

$\begin{bmatrix}2x-\dfrac{3}{4}=3\\ 5x-2y=7\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:2x-\dfrac{3}{4}=3$

$\mathrm{Add\:}\dfrac{3}{4}\mathrm{\:to\:both\:sides}$

$2x-\dfrac{3}{4}+\dfrac{3}{4}=3+\dfrac{3}{4}$

$\mathrm{Simplify}$

$2x=\dfrac{15}{4}$

$\mathrm{Divide\:both\:sides\:by\:}2$

$\dfrac{2x}{2}=\dfrac{\dfrac{15}{4}}{2}$

$\mathrm{Simplify}$

$x=\dfrac{15}{8}$

$\mathrm{Subsititute\:}x=\dfrac{15}{8}$

$\begin{bmatrix}5\cdot \dfrac{15}{8}-2y=7\end{bmatrix}$

$\mathrm{Isolate}\:y\:\mathrm{for}\:5\dfrac{15}{8}-2y=7$

$\mathrm{Subtract\:}5\dfrac{15}{8}\mathrm{\:from\:both\:sides}$

$5\cdot \dfrac{15}{8}-2y-5\cdot \dfrac{15}{8}=7-5\cdot \dfrac{15}{8}$

$\mathrm{Simplify}$

$-2y=-\dfrac{19}{8}$

$\mathrm{Divide\:both\:sides\:by\:}-2$

$\dfrac{-2y}{-2}=\dfrac{-\dfrac{19}{8}}{-2}$

$\mathrm{Simplify}$

$y=\dfrac{19}{16}$

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

$y=\dfrac{19}{16},\:x=\dfrac{15}{8}$