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Mathematics
y = 3 x 6 x 4 y = 28 {:[y=-3x-6],[],[x-4y=-28]:}
Plot two lines by clicking the graph. Click a line to delete it.
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First, we can rearrange the second equation by adding 4 y 4y to both sides:
x 4 y = 28 x = 4 y 28 x-4y=-28=>x=4y-28
Now we can substitute this expression for x x into the first equation:
y = 3 ( 4 y 28 ) 6 y=-3(4y-28)-6
Simplifying this equation gives:
y = 12 y + 90 y=-12 y+90
Adding 12 y 12 y to both sides gives:
13 y = 90 13 y=90
Dividing both sides by 13 gives:
y = 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 ( 90 13 ) 28 = 4 ( 90 ) 364 13 = 16 13 x=4((90)/(13))-28=(4(90)-364)/(13)=(16)/(13)
Therefore, the solution to the system is ( x , y ) = ( 16 13 , 90 13 ) (x,y)=((16)/(13),(90)/(13)).
To plot these lines, we first need to find their slope-intercept forms:
y = 3 x 6 y = 3 x + ( 6 ) y=-3x-6=>y=-3x+(-6)
This equation is in slope-intercept form y = m x + 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 ( 0 , 6 ) (0,-6) and ( 1 , 9 ) (1,-9) that we can use to draw the line.
For the second equation, we rearranged it to x = 4 y 28 x=4y-28, which also gives us the slope-intercept form:
x = 4 y 28 x = 4 y + ( 28 ) 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 ( 28 , 0 ) (-28,0) and ( 24 , 1 ) (-24,1) that we can use to draw the line.
Here is a graph of the two lines:
image.png

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