Question

Dimitri determined that the 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

(2, -2) doesn't work for the second equation, because it would turn out 14=6

Answer 2

It is given that , ordered pair (2, –2) is a solution to the system of linear equations ,

1.---:7 x + 9 y = –4 ------×5

and 2.--: 5 x – 2 y = 6 ------×7

Substituting the value of x=2 and y=-2, in equation 1 and 2 whether this ordered pair satisfy both equation 1 and 2.

L H S

7 × 2 + 9 × (-2)

=14 -18

= -4

=R HS

Equation 2 , L HS

⇒5 x - 2 y

5 ×2 -2×(-2)

=10 +4

=14

≠R HS

As, point (2,-2) does not satisfy equation 2.So, Dimitri must have made calculation mistake while solving equation 1 and equation 2.

1.---:7 x + 9 y = –4 ------×5

and 2.--: 5 x – 2 y = 6 ------×7

5×Equation (1)- 7×Equation (2)

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

59 y= -62

`y=(-62)/(59)`

2×equation 1 +9×equation 2

⇒14 x +18 y+45 x -18 y=-8+54

⇒59 x=46

`x=(46)/(59)`

So, (x,y)=

`x=(46)/(59),y=(-62)/(59)`

are the solution of this equation.