# If (a+2b 2a-b) (4 -2) (2c+d c-2d)=(4 -3) Find a, b, c, and d?

## If $\left(a + 2 b , 2 a - b\right) = \left(4 , - 2\right) , \left(2 c + d , c - 2 d\right) = \left(4 , - 3\right)$ Find a, b, c, and d?

##### 1 Answer
Jul 17, 2018

$a = 0 , b = 2 , c = 1 , \mathmr{and} , d = 2$.

#### Explanation:

I hope, the Problem is to find $a , b , c , d , \mathmr{if} ,$

$\left(a + 2 b , 2 a - b\right) = \left(4 , - 2\right) , \mathmr{and} , \left(2 c + d , c - 2 d\right) = \left(4 , - 3\right)$.

$\left(a + 2 b , 2 a - b\right) = \left(4 , - 2\right)$

$\Rightarrow a + 2 b = 4. . . \left(1\right) , \mathmr{and} , 2 a - b = - 2. . . \left(2\right)$.

Subst.ing the value of $a$ from $\left(1\right) \text{ into } \left(2\right)$,

$2 \left(4 - 2 b\right) - b = - 2 \therefore - 5 b = - 10 \therefore b = 2$.

$\therefore a = 4 - 2 b = 4 - 2 \left(2\right) = 0$.

Thus, $a = 0 , b = 2$.

Similarly, $c = 1 , d = 2$.