Systems of linear equations and inequalities

1003020301

Level:

R \times R

, find the solution set of the equation:

2 x - \frac{x + 2 y}{3} = 2 + \frac{8}{3} y

{[2 y + \frac{6}{5}; y], y \in R}

{[2 y + \frac{6}{5}; \frac{x}{2} - \frac{3}{5}], x \in R, y \in R}

{[\frac{6 + 6 y}{5}; y], y \in R}

\emptyset

1003020302

Level:

Assuming

[x; y] \in R \times R

, solve the equation

x - y - \frac{x - y}{2} = \frac{x - y}{3}

Decide which of the answers below does not express the set of roots.

{[x; y], x \in R, y \in R}

{[x; x], x \in R}

{[y; y], y \in R}

{[t; t], t \in R}

1003020303

Level:

Find the solution set of the equation

1 - \frac{x - 2 y}{4} = x + \frac{y + 2}{2}

R \times R

{[0; y], y \in R}

{[x; y], x \in R, y \in R}

{[\frac{- 4 y}{5}; y], y \in R}

{0}

\emptyset

1003020304

Level:

Find the solution set of the equation

1 - [4 x + 3 \cdot (x - y)] = \frac{1 - 14 x}{2} - \frac{3 - 6 y}{2}

R \times R

\emptyset

{[x; y], x \in R, y \in R}

{[x; \frac{1}{3} + x], x \in R}

{[x; - \frac{1}{3}], x \in R}

1003083001

Level:

Identify which of the following systems of equations has infinitely many solutions.

\begin{aligned} \frac{1}{3} x - 4 y & = 2 \\ - \frac{x}{4} + 3 y & = - \frac{3}{2} \end{aligned}

\begin{aligned} \frac{1}{3} x - 4 y & = 2 \\ - x + 12 y & = 6 \end{aligned}

\begin{aligned} \frac{1}{3} x - 4 y & = 2 \\ \frac{x}{4} - 6 y & = 6 \end{aligned}

\begin{aligned} \frac{1}{3} x - 4 y & = 2 \\ \frac{x}{3} - 4 y & = 0 \end{aligned}

1003083002

Level:

Identify which of the sets is not the solution set of the following system of equations.

\begin{aligned} \frac{1}{2} x - y & = 3 \\ \frac{x}{3} - \frac{2}{3} y & = 2 \end{aligned}

{[6 + 2 y; \frac{x - 6}{2}] : x \in R, y \in R}

{[x; \frac{x - 6}{2}] : x \in R}

{[6 + 2 y; y] : y \in R}

{[2 t; t - 3] : t \in R}

1003083003

Level:

Find the solution set of the following system of equations.

\begin{aligned} \frac{2}{3} x - \frac{1}{2} y & = 1 \\ - 2 x + \frac{3}{2} y & = - 3 \end{aligned}

{[x; \frac{4 x - 6}{3}] : x \in R}

{[x; y] : x \in R, y \in R}

\emptyset

{[0; - 2]}

2000004001

Level:

Identify which of the following systems of equations has infinitely many solutions.

\begin{aligned} x - y & = 5 \\ 2 x - 2 y & = 10 \end{aligned}

\begin{aligned} x - y & = 5 \\ 3 x - 3 y & = 10 \end{aligned}

\begin{aligned} x - y & = 5 \\ - x + y & = 5 \end{aligned}

\begin{aligned} x - y & = 5 \\ 2 x + 2 y & = 10 \end{aligned}

2000004002

Level:

Identify which of the following systems of equations has infinitely many solutions.

\begin{aligned} 2 y & = 5 x - 3 \\ y & = \frac{5}{2} x - \frac{3}{2} \end{aligned}

\begin{aligned} 2 y & = 5 x - 3 \\ y & = \frac{5}{3} x - \frac{3}{2} \end{aligned}

\begin{aligned} 2 y & = 5 x - 3 \\ y & = \frac{5}{4} x - 1 \end{aligned}

\begin{aligned} 2 y & = 5 x - 3 \\ - y & = \frac{5}{2} x + \frac{3}{2} \end{aligned}

2000004003

Level:

Identify which of the following systems of equations has no solution.

\begin{aligned} x + 3 y & = 11 \\ 5 x + 15 y & = 33 \end{aligned}

\begin{aligned} x + 3 y & = 11 \\ 5 x + 15 y & = 55 \end{aligned}

\begin{aligned} x + 3 y & = 11 \\ 3 x + 12 y & = 33 \end{aligned}

\begin{aligned} x + 3 y & = 11 \\ - x + 3 y & = 11 \end{aligned}

Systems of linear equations and inequalities

1003020301

1003020302

1003020303

1003020304

1003083001

1003083002

1003083003

2000004001

2000004002

2000004003

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