Answer:
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
[tex]y=\frac{-62}{59}[/tex]
2×equation 1 +9×equation 2
⇒14 x +18 y+45 x -18 y=-8+54
⇒59 x=46
[tex]x=\frac{46}{59}[/tex]
So, (x,y)=
[tex]x=\frac{46}{59},y=\frac{-62}{59}[/tex]
are the solution of this equation.
