Question

Solve graphically each of the following systems of linear equations. Also, find the coordinates of the points where the lines meet the axis of x in each system.

(i) 2x + y = 6
x − 2y = −2

(ii) 2x − y = 2
4x − y = 8

(iii) x + 2y = 5
2x − 3y = −4

(iv) 2x + 3y = 8
x − 2y = −3

Answer 1

(i)

The given equations are

_{The two points satisfying (i) can be listed in a table as,}

	4	0
	−2	6

_{The two points satisfying (ii) can be listed in a table as,}

	4	6
	3	4

Now, graph of equations (i) and (ii) can be drawn as,

It is seen that the solution of the given system of equations is given by x = 2, y = 2.

Also, it is observed that the coordinates of the points where the lines (i) and (ii) meet the x-axis are respectively.

(ii) The given equations are

_{The two points satisfying (i) can be listed in a table as,}

	0	2
	2	2

_{The two points satisfying (ii) can be listed in a table as,}

	1	3
	–4	4

Now, graph of equations (i) and (ii) can be drawn as,

It is seen that the solution of the given system of equations is given by x = 3, y = 4.

Also, it is observed that the coordinates of the points where the lines (i) and (ii) meet the x-axis are respectively.

(iii) The given equations are

_{The two points satisfying (i) can be listed in a table as,}

	0	−1
	2.5	3

_{The two points satisfying (ii) can be listed in a table as,}

	4	–5
	4	–2

Now, graph of equations (i) and (ii) can be drawn as,

It is seen that the solution of the given system of equations is given by x = 1, y = 2.

Also, it is observed that the coordinates of the points where the lines (i) and (ii) meet the x-axis are respectively.

Solution is missing

(iv) The given equations are

_{The two points satisfying (i) can be listed in a table as,}

	–2	7
	4	–2

_{The two points satisfying (ii) can be listed in a table as,}

	–1	3
	1	3

Now, graph of equations (i) and (ii) can be drawn as,

It is seen that the solution of the given system of equations is given by x = 1, y = 2.

Also, it is observed that the coordinates of the points where the lines (i) and (ii) meet the x-axis are respectively.