Question

Draw the graphs of the following linear equations on the same graph paper:
2x + 3y = 12, x - y = 1
Find the coordinates of the vertices of the triangle formed by the two straight lines and
the y-axis. Also, find the area of the triangle​

Answer 1

Graph of the Equations :

$\huge\blue{ 2x {}^{2} - 3y - 12 = 0}$

we have

$2x + 3y = 12$

$2x = 12 - 3y$

$x = \frac{12 - 3y}{2}$

Putting y= 4

we get

$x = \frac{12 - 3 \times 4}{2} = 0$

Putting y= 2

we get

$x = \frac{12 - 3 \times 2}{2}$

Thus we have following table for the line of

$2x - 3y = 12$

$\frac{ |x | \: \: |0 | \: \: |3| }{ |y | \: |4| \: \: |2| }$

Plotting points A(0,4) B(3,2) on the graph

Similarly Obtaining values of

$x - y = 1$

$\frac{ |x| \: |1| \: |0| }{ |y| \: |0| \: | - 1| }$

Plotting point C(1,0) and D(0,-1) on graph

$\huge\pink{ look \: in \: the \: graph}$

The graph of time 2x+3y=12 intersect with y axis at B (0,4) and the graph of the line

X-y=1 intersect with y axis at C(0,-1)

So, the vertices of the triangle formed by two straight lines and y axis

Now

$area = \frac{1}{2} \times (base \times height)$

$= \frac{1}{2} (bc \times ab)$

$= \frac{1}{2} \times (5 + 3)$

$= \frac{15}{2} unit {}^{2}$

Hope it is helpful

Hope it is helpful please mark me as brainlest