Question

Please help me with both of these questions I’m supper stuck

Answer 1

Answer:

ONE SOLUTION

Step-by-step explanation:

When two points on a line are given, the equation of the line is given by the formula:

             $\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$

where $(x_1, y_1)$ and $(x_2, y_2)$ are the points on the line.

Here, the first set of points are: $(-1, 3)$ and $(0, 1)$.

Therefore, $(x_1, y_1) = (-1, 3)$ and $(x_2,y_2) = (0, 1)$.

The line passing through this is given by:

$\frac{y - 3}{1 - 3} = \frac{x + 1}{1}$

$\implies y - 3 = -2x - 2$

∴ 2x + y - 1 =0

Now, for the second line, the points are:

$(x_1, y_1) = (1, 4)$ and $(x_2, y_2) = (0, 2)$.

Therefore, $\frac{y - 4}{-2} = \frac{x - 1}{-1}$

$\implies -y + 4 = -2x + 2$

∴ 2x - y + 2 = 0

Now, to determine the number of solutions the two equations have, we solve these two equations,

Adding Eqn(1) and Eqn(2) we get:

4x = -1

$\implies x = \frac{-1}{4}$

And $y = \frac{3}{2}$.

Since, we arrive at unique values of 'x' and 'y', we say the lines have only one unique solution.