Question

linear in two variables
$2x +5 y = 12 \: and \: 3x - 6y = 11$
​

Answer 1

Solve $2x+5y=12$ and $3x-6y=11$

Definition:

The solution of an equation is the set of all values that,when substituted for unknowns ,make an equation true.

Step-by-step explanation:

$2x+5y=12$           (1)

$3x-6y=11$          (2)

Multiply equation (1) by 3 and equation (2) by 2,

$6x+15y=36\\6x-12y=22$

Subtract these two equations,

$6x+15y=36\\6x-12y=22$

(-)   (+)       (-)

____________

$27y=14\\y=\frac{14}{27}\\ y=0.52$

Substitue the value of y in equation (1)

$2x+5y=12\\2x+5(\frac{14}{27})=12\\ 2x+\frac{70}{27}=12\\ 2x=12-\frac{70}{27}\\2x=\frac{254}{27} \\x=\frac{127}{27}$

Therefore,the value of x is 127/27 and y is 14/27