Question

solve the equations 2x-y=5,3x+2y=11 in cross multiplication method​

Answer 1

Question -

Solve the following pair of equations by cross multiplication method-

2x-y=5

3x+2y=11

Solution -

Given equations,

2x-y=5

2x-y-5=0

And,

3x+2y=11

3x+2y-11=0

Here,

$a_1 = 2$

$b_1 = - 1$

$c_1 = - 5$

$a_2 = 3$

$b_2 = 2$

$c_2 = - 11$

We know that,

$x = \frac{b_1c_2 - b_2c_1}{a_1b_2 - a_2b_1}$

Putting the values we will get -

$x = \frac{ - 1 \times ( - 11) - 2 \times ( - 5)}{2 \times 2 - 3 \times ( - 1)}$

$x = \frac{11 + 10}{4 + 3}$

$x = \frac{21}{7}$

$\boxed{\boxed{{\rm \: x = 3}}}$

And,

$y = \frac{c_1a_2 - c_2a_1}{a_1b_2 - a_2b_1}$

Putting the values we will get -

$y = \frac{ - 5 \times 3 - ( - 11) \times 2}{2 \times 2 - 3 \times ( - 1)}$

$y = \frac{ - 15 + 22}{4 + 3}$

$y = \frac{7}{7}$

$\boxed{\boxed{{\rm \: y = 1}}}$