Question

# x-y=-2 (1,3) 3x-y=-2 is the ordered pair a solution of the system of linear equations. or not a solution

Forms of linear equations
$$\displaystyle{x}-{y}=-{2}{\left({1},{3}\right)}$$
$$\displaystyle{3}{x}-{y}=-{2}$$
is the ordered pair a solution of the system of linear equations.
or not a solution

2021-01-28

Given
$$\displaystyle{x}-{y}=-{2}---{\left({1}\right)}$$
$$\displaystyle{3}{x}-{y}=-{2}---{\left({2}\right)}$$
From equation(1),we get the value of x in terms of y as
$$\displaystyle{x}-{y}=-{2}$$
$$\displaystyle{x}={y}=-{2}----{\left({3}\right)}$$
on substituting value of $$x=y-2$$ from eq(3) to q(2),we get the value of y as
$$\displaystyle{3}{\left({y}-{2}\right)}-{y}=-{2}$$
$$\displaystyle{3}{y}-{6}-{y}=-{2}$$
$$\displaystyle{2}{y}={4}$$
$$\displaystyle{y}={2}$$
Now substitute value of $$y=2$$ in eq(3),we get value of x as
$$\displaystyle{x}={2}-{2}$$
$$\displaystyle{x}={0}$$
Hence (0,2) is an ordered pair solution, not (1,3)