Find the other equation — task. Maths TNSB Mentoring, Class 9.

Find two linear equations for equation

2 x + 3 y = - 5

, which satisfies the condition of unique solution, infinitely many solutions and no solution.

Solution:

For a system of equations to be a unique solution, the equations must satisfy the condition is

and the system of equations is

For a system of equations to have infinitely many solutions, the equations must satisfy the condition is

and the system of equaiton is

For a system of equations to have no solutions, the equations must satisfy the condition is

and the system of equations is

Answer variants:

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

\begin{array}{l} 6 x + 9 y = - 15 \\ 8 x + 12 y = - 20 \end{array}

\begin{array}{l} 6 x + 9 y = - 6 \\ 8 x + 12 = - 7 \end{array}

\begin{array}{l} 3 x - 4 y = 6 \\ 2 x + 5 y = 1 \end{array}

\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

Did you find an error?

8. Find the other equation