**Goa Board Class 10 Solutions for Mathematics – Linear equations in two variables (English Medium)**

**Exercise 3A:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

Since the two graphs intersect at (2, 3),

x = 2 and y = 3.

**Solution 6:**

**Solution 7:**

Since the two graphs intersect at (2, -3),

x = 2 and y = -3.

**Solution 8:**

Since the two graphs intersect at (-2, 3),

x = -2 and y = 3.

**Solution 9:**

Since the two graphs intersect at (-1, 2),

x = -1 and y = 2.

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Solution 14:**

**Solution 15:**

**Solution 16:**

**Solution 17:**

**Solution 18:**

**Solution 19:**

**Solution 20:**

**Solution 21:**

**Solution 22:**

Since the graph of the system of equations is coincident lines, the system has infinitely many solutions.

**Solution 23:**

**Solution 24:**

**Solution 25:**

Since the graph of the system of equations is coincident lines, the system has infinitely many solutions.

**Solution 26:**

Since the graph of the system of equations is parallel lines, the system has no solution and hence is inconsistent.

**Solution 27:**

Since the graph of the system of equations is parallel lines, the system has no solution and hence is inconsistent.

**Solution 28:**

Since the graph of the system of equations is parallel lines, the system has no solution and hence is inconsistent.

**Solution 29:**

**Exercise 3B:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Solution 14:**

**Solution 15:**

**Solution 16:**

**Solution 17:**

**Solution 18:**

**Solution 19:**

**Solution 20:**

**Solution 21:**

**Solution 22:**

**Solution 23:**

**Solution 24:**

**Solution 25:**

**Solution 26:**

**Solution 27:**

**Solution 28:**

**Solution 29:**

**Solution 30:**

**Solution 31:**

**Solution 32:**

**Solution 33:**

**Solution 34:**

**Solution 35:**

**Solution 36:**

**Solution 37:**

**Solution 38:**

**Solution 39:**

**Solution 40:**

**Solution 41:**

**Solution 42:**

**Solution 43:**

**Solution 44:**

**Solution 45:**

**Solution 46:**

**Solution 47:**

**Solution 48:**

**Solution 49:**

**Solution 50:**

**Exercise 3C:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Exercise 3D:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Solution 14:**

**Solution 15:**

**Solution 16:**

**Solution 17:**

Thus, k = 2, is the common value for which there are infinitely many solutions

**Solution 18:**

**Solution 19:**

**Solution 20:**

**Solution 21:**

**Solution 22:**

**Solution 23:**

**Solution 24:**

**Solution 25:**

**Solution 26:**

**Solution 27:**

**Solution 28:**

**Solution 29:**

**Solution 30:**

**Solution 31:**

**Exercise 3E:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Solution 14:**

**Solution 15:**

**Solution 16:**

**Solution 17:**

**Solution 18:**

**Solution 19:**

**Solution 20:**

**Solution 21:**

**Solution 22:**

**Solution 23:**

**Solution 24:**

**Solution 25:**

**Solution 26:**

**Solution 27:**

**Solution 28:**

**Solution 29:**

**Solution 30:**

**Solution 31:**

**Solution 32:**

**Solution 33:**

**Solution 34:**

**Solution 35:**

**Solution 36:**

**Solution 37:**

**Solution 38:**

**Solution 39:**

**Solution 40:**

**Solution 41:**

**Solution 42:**

**Solution 43:**

**Solution 44:**

**Solution 45:**

**Solution 46:**

**Solution 47:**

**Solution 48:**

**Solution 49:**

**Solution 50:**

**Solution 51:**

**Solution 52:**

**Solution 53:**

**Exercise 3F:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Solution 14:**

**Solution 15:**

**Solution 16:**

**Solution 17:**

**Solution 18:**

**Solution 19:**

**Solution 20:**

**Solution 21:**

**Exercise MCQ:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Solution 14:**

**Solution 15:**

**Solution 16:**

**Solution 17:**

**Solution 18:**

**Solution 19:**

**Solution 20:**

**Solution 21:**

**Solution 22:**

**Solution 23:**

**Solution 24:**

**Solution 25:**

**Solution 26:**

**Solution 27:**

**Exercise FA:**

**Solution 1:**

**Solution 2:**

**Solution 3:**

**Solution 4:**

**Solution 5:**

**Solution 6:**

**Solution 7:**

**Solution 8:**

**Solution 9:**

**Solution 10:**

**Solution 11:**

**Solution 12:**

**Solution 13:**

**Solution 14:**

**Solution 15:**

**Solution 16:**

**Solution 17:**

**Solution 18:**

**Solution 19:**

**Solution 20:**

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