Question

please find the ans fast!

Answer 1

Given,
x +2y = 7
and ,
2x - y =4.
Now take euqation first.
x+2y= 7.
when , x= 7 :-y= 0 points will be (7,0)
when x= -1 , y= 4 . point's will be (-1,4)
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now take second euqation,
2x-y=7
when , x=2,y= 0 points will be (2,0)
when , x= 0, y= -4 points will be (0,-4)
.........................................................................
see picture for graph!
by observing we get lines intersect at point (3,2)
so
x=
y=2.
hope this helps you!!

Answer 2

We are given a pair of linear equations in two variables. To find a solution graphically, we first plot the two lines on a Cartesian Plane and find the point of intersection.

We also need the points where the line meets Y-Axis. 


The point where the line meets Y-axis, has it's x-coordinate as zero. So, by putting $x=0$, we can find the point where the lines meet Y-axis.

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The first line is:

$\boxed{x+2y-7=0} \\ \\ \\ \implies 2y=7-x \\ \\ \\ \implies y = \frac{7-x}{2}$

Let us first put $x=0$

$y=\frac{7-x}{2} = \frac{7-0}{2} = \frac{7}{2} \\ \\ \implies y = 3.5$

Thus, (0,3.5) lies on the line. 

We need one more point to plot the line. 

Let us take $x=7$

Then

$y=\frac{7-x}{2} = \frac{7-7}{2} = \frac{0}{2} = 0$

Thus, (7,0) also lies on the line. 

Now, we can join the points (0,3.5) and (7,0) to plot the graph of $x+2y-7=0$


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Now, the second line is:

$\boxed{2x-y-4=0} \\ \\ \implies y = 2x-4$


Let us first put $x=0$

$y=2x-4 = 2(0)-4 = 0-4 = -4$


Thus, (0,-4) lies on the line.


Now, let us put $x=2$

$y=2x-4 = 2(2)-4 = 4-4 = 0$

Thus, (2,0) lies on the line.

So, by joining (0,-4) and (2,0), we obtain the graph of $2x-y-4=0$


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The graph is attached. We see that the two lines intersect at a point.

The Point of Intersection is  $\textbf{(3,2)}$


Thus, the solution of the equations is:

$\textbf{x=3 , y=2}$



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FINAL SUMMARY:


Point of Intersection of Lines is (3,2)

$\textbf{x+2y-7=0 }$  meets the Y-axis at (0,3.5)

$\textbf{2x-y-4=0 }$  meets the Y-axis at (0, - 4)