Question

Here is a system of equations. y = - 3x - 4, y = - x - 2 Graph the system. Then write its solution Note that you can also answer No solutionor "Infinitely many" solutions

Answer 1

Answer;

$(-1,-1)$

Explanation;

Here, we want to get the solution a pair of linear equation which we are to solve simultaneously by the graphical method

We need to plot the graphs of these two lines; The point at which the lines meet will represent the solution to the system of linear equations

The general equation of a straight line is;

$y=mx\text{ + b}$

where m is the slope and b is the y-intercept

To plot the lines, we need the x-intercepts and the y-intercepts

This refer to the point at which the line touches the x and y axes respectively

Let us take the lines one after the other;

$y=-3x-4$

The y-intercept here is -4; so the point is (0,-4)

To get the x-intercept value, we simply set y to zero and get the value of x

$\begin{gathered} 0=-3x-4 \\ -3x=4 \\ x\text{ = }\frac{-4}{3} \end{gathered}$

So the x-intercept is (-4/3,0)

To plot the line; we simply join (0,-4) and (-4/3,0)

For the second line;

We have the y-intercept as -2

So the point is (0,-2)

To get the x-intercept, we simply set y to 0 and solve for x

$\begin{gathered} 0=-x-2 \\ x=-2 \end{gathered}$

So, the x-intercept point is (-2,0)

We can now join (0,-2) and (-2,0) to represent the second line

Proceeding, we get the lines on the cartesian grid

This is shown in the attachment below;

As we can see from the plot, the lines touch at the point (-1,-1) and that represents the solution to the equation