Question

Which choice is the solution for this system ? 2x − 5y = 14 x + 3 2 y = 5

Answer 1

Answer:

The required solution is (5.75,-0.5). It can be written as $(\frac{11}{4},-\frac{1}{2})$.

Step-by-step explanation:

The given equations are

$2x-5y=14$                       .... (1)

$x+\frac{3}{2}y=5$            .... (2)

Multiply the equation (2) by 2.

$2x+3y=10$                     .... (3)

Subtract equation (1) from equation (3).

$2x+3y-(2x-5y)=10-14$

$2x+3y-2x+5y=-4$

$8y=-4$

$y=-\frac{1}{2}=-0.5$

Put this value in equation (1).

$2x-5(-0.5)=14$

$2x+2.5=14$

$2x=11.5$

$x=5.75$

Therefore the required solution is (5.75,-0.5). It can be written as $(\frac{11}{4},-\frac{1}{2})$.