Question

Using the elimination method, solve each of the
following pairs of simultaneous equations.


please solve at least two of them.
​

Answer 1

$Using the elimination method, solve each of the</p><p>following pairs of simultaneous equations.</p><p></p><p>please solve at least two of them.</p><p>}$

Using the elimination method, solve each of the

following pairs of simultaneous equations.

please solve at least two of them.

Answer 2

Step-by-step explanation:

(a)

$\frac{x + 1}{y + 2} = \frac{3}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: eq .1 \\ \frac{x - 2}{y - 1} = \frac{3}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:eq.2$

$eq.1 \\ (x + 1)4 = 3(y + 2) \\ 4x + 4 = 3y + 6 \\ 4x - 3y = 6 - 4 \\4x - 3y = 2 \\ eq.2 \\ (x - 2)5 = 3(y - 1) \\ 5x - 10 = 3y - 3 \\ 5x - 3y = 10 - 3 \\ 5x - 3y = 7$

Now,

Subtracting eq.1 from eq.2 :-

$\ 5x - 3y = 7 \\ - (4x - 3y = 2) \\ 5x - 4x - 3y + 3y = 7 - 2 \\ x = 5$

Now, by substituting the value of x in eq.1

$4x - 3y = 2 \\ 4(5) - 3y = 2 \\ 20 - 3y = 2 \\ 20 - 2 = 3y \\ 18 \div 3 = y \\ y = 6$

Hence value of x is 5 and y is 6

(b)

$\: \frac{x}{3} - \frac{y}{2} = \frac{5}{6}\: \: \: eq.1 \\3x - \frac{2}{5} y =3 \frac{2}{5} \: \: \: eq.2$

Now,eq. 1:-

$\frac{2x - 3y}{6} = \frac{5}{6} \\ 2x - 3y = 5$

And ,eq.2:-

$\frac{15x - 2y}{5} = \frac{17}{5} \\ 15x - 2y = 17$

Now by multiplying eq.1 from 2 and eq.2 from 3 , we get,

$eq.1 \\ (2x \times 2) - (3y \times 2) = (5 \times 2) \\ 4x - 6y = 10 \\ eq.2 \\ (15x \times 3) - (2y \times 3) = (17 \times 3) \\ 45x - 6y = 51$

Now by subtracting EQ.1 from eq.2:-

$45x - 6y = 51 \\ - (4x - 6y = 10)$

we get,

$45x - 4x + 6y - 6y = 51 - 10 \\ 41x = 41 \\ x = 1$

by substituting the value of x in eq.1:-

$2x - 3y = 5 \\ 2(1) - 3y = 5 \\ - 3y = 5 - 2 \\ -3y= 3 \\ y = \frac{3}{ - 3} \\ y = - 1$

hence the value of x is 1 and the value of y is-1