Activity 1.1.3

Which of the following equations are linear? Please provide a justification for your response.

1. $$2x + xy -3y^2 = 2$$.

2. $$-2x_1 + 3x_2 +4x_3 - x_5 = 0$$.

3. $$x = 3z - 4y$$.

Consider the system of linear equations: $$\begin{alignedat}{4} x & {}+{} & y & & & {}={} & 3 \\ & & y & {}-{} & z & {}={} & 2 \\ 2x & {}+{} & y & {}+{} & z & {}={} & 4. \\ \end{alignedat}$$

1. Is $(x,y,z) = (1,2,0)$ a solution?

2. Is $(x,y,z) = (-2,1,0)$ a solution?

3. Is $(x,y,z) = (0,-3,1)$ a solution?

4. Can you find a solution in which $y = 0$?

5. Do you think there are other solutions? Please explain your response.