Question

Mathematics

Plot two lines by clicking the graph. Click a line to delete it.

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Best Answer

First, we can rearrange the second equation by adding to both sides:

Now we can substitute this expression for into the first equation:

Simplifying this equation gives:

Adding to both sides gives:

Dividing both sides by 13 gives:

Now we can use either equation to solve for . Let’s use the rearranged second equation:

Therefore, the solution to the system is .

To plot these lines, we first need to find their slope-intercept forms:

To plot these lines, we first need to find their slope-intercept forms:

This equation is in slope-intercept form where is the slope and is the -intercept. So the slope of this line is and the -intercept is . To plot the line, we can start at the -intercept and then use the slope to find another point on the line. For example, if we move one unit to the right (i.e., increase by 1), we will move 3 units down (i.e., decrease by 3). This gives us the points and that we can use to draw the line.

For the second equation, we rearranged it to , which also gives us the slope-intercept form:

For the second equation, we rearranged it to

So the slope of this line is and the -intercept is . To plot this line, we can start at the -intercept and then use the slope to find another point on the line. For example, if we move one unit up (i.e., increase by 1), we will move 4 units to the right (i.e., increase by 4). This gives us the points and that we can use to draw the line.

Here is a graph of the two lines:

Blue line represents and orange line represents .

Here is a graph of the two lines:

Blue line represents