Question

Dimitri determined that he ordered pair (2,-2) is a solution to the system of linear equations 7x +9y=-4 and 5x -2y=6 as shown What was dimitri's mistake?

Answer 1

Answer:

Therefore $(\frac{46}{59},-\frac{62}{59} )$ is a solution of given liner equations.

Step-by-step explanation:

Given system of equation are

7x+9y=-4..............(1)

5x-2y=6...............(2)

Equation (1)×5 - equation (2)×7

35x +45y-(35x-14y)= -20-42

⇔ 35x+45y-35x+14y = -62

⇔59 y = -62

$\Leftrightarrow y =-\frac{62}{59}$

Putting the value of y in equation (1)

$7x +9.(-\frac{62}{59} )= -4$

$\Leftrightarrow 7x += -4+\frac{558}{59}$

$\Leftrightarrow 7x = \frac{322}{59}$

$\Leftrightarrow x =\frac{322}{59\times 7}$

$\Leftrightarrow x =\frac{46}{59}$

Therefore  $x =\frac{46}{59}$ and  $y =-\frac{62}{59}$

Therefore $(\frac{46}{59},-\frac{62}{59} )$ is a solution of given liner equations.