Substitution method to solve a pair of linear equations in two variables

On solving pairs of linear equations, the solutions obtained are given below. Indicate in which case the use of graphical method for solution would not have been convenient.

• x = 0, y = - 1

• x = 15/19, y = 17/19

• x = - 2 y = 3

• x = - 16 y = - 22

Answer explanation

The graphical method is not convenient in cases when the point representing the solution of the linear equations has non-integral coordinates like ( √3, 2√ 7 ) , (–1.75, 3.3), (4/13 , 1/13), etc. There is every possibility of making mistakes while reading such coordinates. Hence option 2 is the correct answer.

For the equation, 7x - 3y = 2, express x in terms of y.

• x = ( 2 + 3y) / 7

• y = (2 -7x) / - 3

• x = ( 2 - 3y) / 7

• x = ( 2 + 3y)

Answer explanation

For the equation,7x - 3y = 2, 7x = 2 + 3y Hence, x = (2 + 3y) / 7 So, option 1 is correct

Use Substitution method to solve the following equations -- 3x + 4y = - 4 x + 2y = 2

• x = 0 y = 1

• x = - 8 y = 5

• x = - 18 y = 10

Answer explanation

3x + 4y = -4 ……… (1) x + 2y = 2 ……….. ( 2) From Eq. 2, x = 2 - 2y ………….(3) Substituting value of x in Eq. 1, 3 (2 -2y) + 4y = - 4 6 -6y +4y = -4 -2y = -4 -6 = - 10 -2y = -10 ............... (4) y = 10/2 = 5 Substituting value of y in Eq. 3, x = 2 -10 = -8 So correct option is x = - 8, y = 5

Use Substitution method to solve the following equations -- 4x + 3y = - 3 8x + 6y + 6 = 0

• x = 0 y = - 1

• No solution

• Infinite solutions

Answer explanation

4x + 3y = - 3 ……… (1) 8x + 6y = -6 ……….. ( 2) From Eq. 1, 3y = -3 - 4x ………….(3) y = ( -3 - 4x) / 3 Substituting value of y in Eq. 2, 8x + 6 (-3 -4x) /3 = - 6 8x + 2 ( - 3 - 4x) = - 6 8x -6 - 8x = - 6 - 6 = - 6 This is a True statement without variables and so the equations have Infinite number of solutions. So correct option is Option 3

The larger of two complementary angles exceeds the smaller by 22°. If y is the larger angle and x is the smaller angle, find the angles.

• x = 79° y = 101°

• x = 56° y = 34°

• x = 34° y = 56°

• x = 101° y = 79°

Answer explanation

x + y = 90 …..(1) Complementary angles y = x + 22 ……(2) Substituting value of y from Eq. 2 in eq.1 , x + x + 22 = 90 2x = 90 -22 = 68 x = 34 Substituting value of x in Eq. 1, 34 + y = 90 y = 90 - 34 = 56 Answer --- y = 56° , x = 34°

The Perimeter of an isosceles triangle is 24 cm. The length of it's congruent sides is 13 cm less than twice the length of the base. Find the length of base and the length of congruent side.

• Base = 10 cm Side = 7 cm

• Base = 11/3 cm Side = 61/3 cm

• Base = 7 cm Side = 10 cm

Answer explanation

Let side = x, base = y Perimeter of Triangle = 2x + y 2x + y = 24 ---------- (1) x = 2y -13 --, -------(2) Substituting value of x from Eq. 2 into Eq.1, 2 ( 2y - 13) + y = 24 4y - 26 + y = 24 5y = 50 y = 10 Substituting value of y in eq. 2, x = 20 - 13 = 7 Hence Base = 10 , side = 7