Question

Solve graphically each of the following systems of linear equations. Also find the coordinates of the points where the lines meet axis of y.

(i) 2x − 5y + 4 = 0,
2x + y − 8 = 0

(ii) 3x + 2y = 12,
5x − 2y = 4

(iii) 2x + y − 11 = 0,
x − y − 1 = 0

(iv) x + 2y − 7 = 0,
2x − y − 4 = 0

(v) 3x + y − 5 = 0,
2x − y − 5 = 0

(vi) 2x − y − 5 = 0,
x − y − 3 = 0

Answer 1

(i) The given equations are

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

	−2	8
	0	4

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

	4	2
	0	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 = 2.

Also, it is observed that the lines (i) and (ii) meet the y-axis at the points respectively.

(ii) The given equations are

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

	4	6
	0	–3

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

	3	2
	5.5	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 = 2, y = 3.

Also, it is observed that the lines (i) and (ii) meet the y-axis at the points respectively.

(iii) The given equations are

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

	3	1
	5	9

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

	1	5
	0	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 = 4, y = 3.

Also, it is observed that the lines (i) and (ii) meet the y-axis at the points respectively.

(iv) The given equations are

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

	5	7
	1	0

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

	2	1
	0	–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 = 3, y = 2.

Also, it is observed that the lines (i) and (ii) meet the y-axis at the points respectively.(v) The given equations are

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

	1	3
	2	–4

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

	1	4
	–3	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 = 2, y = −1.

Also, it is observed that the lines (i) and (ii) meet the y-axis at the points respectively.

(vi) The given equations are

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

	1	3
	–3	1

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

	1	5
	–2	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 = 2, y = −1.

Also, it is observed that the lines (i) and (ii) meet the y-axis at the points respectively.