Question
Mathematics
$\begin{array}{l}y=-3x-6\\ \\ x-4y=-28\end{array}${:[y=-3x-6],[],[x-4y=-28]:}
Plot two lines by clicking the graph. Click a line to delete it.
Solve problem with AI
First, we can rearrange the second equation by adding $4y$4y to both sides:
$x-4y=-28⇒x=4y-28$x-4y=-28=>x=4y-28
Now we can substitute this expression for $x$x into the first equation:
$y=-3\left(4y-28\right)-6$y=-3(4y-28)-6
Simplifying this equation gives:
$y=-12y+90$y=-12 y+90
Adding $12y$12 y to both sides gives:
$13y=90$13 y=90
Dividing both sides by 13 gives:
$y=\frac{90}{13}$y=(90)/(13)
Now we can use either equation to solve for $x$x. Let’s use the rearranged second equation:
$x=4\left(\frac{90}{13}\right)-28=\frac{4\left(90\right)-364}{13}=\frac{16}{13}$x=4((90)/(13))-28=(4(90)-364)/(13)=(16)/(13)
Therefore, the solution to the system is $\left(x,y\right)=\left(\frac{16}{13},\frac{90}{13}\right)$(x,y)=((16)/(13),(90)/(13)).
To plot these lines, we first need to find their slope-intercept forms:
$y=-3x-6⇒y=-3x+\left(-6\right)$y=-3x-6=>y=-3x+(-6)
This equation is in slope-intercept form $y=mx+b$y=mx+b where $m$m is the slope and $b$b is the $y$y-intercept. So the slope of this line is $-3$-3 and the $y$y-intercept is $-6$-6. To plot the line, we can start at the $y$y-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 $x$x by 1), we will move 3 units down (i.e., decrease $y$y by 3). This gives us the points $\left(0,-6\right)$(0,-6) and $\left(1,-9\right)$(1,-9) that we can use to draw the line.
For the second equation, we rearranged it to $x=4y-28$x=4y-28, which also gives us the slope-intercept form:
$x=4y-28⇒x=4y+\left(-28\right)$x=4y-28=>x=4y+(-28)
So the slope of this line is $4$4 and the $y$y-intercept is $-28$-28. To plot this line, we can start at the $y$y-intercept and then use the slope to find another point on the line. For example, if we move one unit up (i.e., increase $y$y by 1), we will move 4 units to the right (i.e., increase $x$x by 4). This gives us the points $\left(-28,0\right)$(-28,0) and $\left(-24,1\right)$(-24,1) that we can use to draw the line.
Here is a graph of the two lines:

Blue line represents $y=-3x-6$y=-3x-6 and orange line represents $x=4y-28$x=4y-28.
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