Question

The graph of the lines $x+y=7$ and $x-y=3$ meet at the point-
A. $\left(5,2\right)$
B. $\left(2,5\right)$
C. $\left(6,3\right)$
D. $\left(-1,4\right)$

Answer 1

Hint- From the given equations, find out the value of y and then start putting the values of x (let’s say 1,2,3) to find out the value of y when x was 1 or 2 or 3. Do the same in the second equation as well and find out the common points in both the values of the equations.

Complete Step-by-step answer:

The equations given in the question are-
$x+y=7$
And
$x-y=3$
Let’s mark both the equations as 1 and 2. We have-
$x+y=7$ $\to$ equation 1
And
$x-y=3$ $\to$ equation 2
For equation 1, the value of y will be-
$y=7-x$
Marking the recent equation as equation 3, we have-
$y=7-x$ $\to$ equation 3
Now, for equation 3, we will put the value of x as 1,2 or 3. Every time, we will get a new value of y:
If $x=1$, then the value of y will be $y=7-1=6$
If $x=2$, then the value of y will be $y=7-2=5$
If $x=3$, then the value of y will be $y=7-3=4$

Now, for equation 2 which is $x-y=3$, the value of y will be as follows-
$y=x-3$
Marking the above equation as equation 4, we have-
$y=x-3$ $\to$ equation 4
Now, again, for equation 4, we will put different values of x to get different values of y:
If $x=1$, then the value of y will be $y=1-3=-2$
If $x=2$, then the value of y will be $y=2-3=-1$
If $x=3$, then the value of y will be $y=3-3=0$
If $x=4$, then the value of y will be $y=4-3=1$
If $x=5$, then the value of y will be $y=5-3=2$
In both the equations, equation 3 and equation 4, $x=5,y=2$ is common. Thus, we draw a graph and it meets the point $\left(5,2\right)$.

Note: While looking for the value of y, keep putting the value of x as 1,2,3 or 4 as long as one common value doesn’t appear. If you mark the equations, remember to put the number of the equation correctly and be careful with the negative and positive signs.