EDGE Math 8

1.	Wilson solved a system of two linear equations in two variables and his computations led to the equation $0 = 3.$ Which of the following statements describes such system?

It has no solution.

It has exactly one solution.

It has an infinite number of solutions.

None of the choices

Answer: It has no solution.

2.	For what values of m and n will the following system of linear equations have an infinite number of solutions?

{\begin{array}{l} x + y = 6 \\ 3 x + (m + n) y = 2 n \end{array}

m = 9 and n = 9

m = −9 and n = −9

m = 6 and n = −9

none of the choices

Answer: none of the choices; $m = - 6$ and $m = 9$

3.	Which of the following ordered pairs is not a solution to the following system of linear equations?

{\begin{cases} - x + y = 1 \\ 2 x - 2 y = - 2 \end{cases}

(−1, 0)

(0, 1)

(1.5, 2.5)

none of the choices

Answer: none of the choices

4.	Which of the following system of linear equations have $(1, 1)$ as its only solution?

{\begin{cases} 6 x - 3 y = 3 \\ 2 x - y = 1 \end{cases}

{\begin{cases} x + y = 2 \\ 2 x - y = 1 \end{cases}

{\begin{cases} x + y = 2 \\ - x - y = 1 \end{cases}

none of the choices

Answer: ${\begin{cases} x + y = 2 \\ 2 x - y = 1 \end{cases}$