Q. 45.0( 2 Votes )

# Solve the following pair of linear equations by the method of cross – multiplication:

(a + b)x + (a — b)y = a^{2} + 2ab — b^{2}, a ≠ b

(a — b) (x + y) = a^{2} — b^{2}, a ≠ b

Answer :

Given equations are

(a + b)x + (a — b)y = a^{2} + 2ab — b^{2}

And (a — b) (x + y) = a^{2} — b^{2}

Change the given equations to the form,

a_{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 …(i)

⇒ (a + b)x + (a — b)y – a^{2} – 2ab + b^{2} = 0

And

(a – b)x + (a – b)y – a^{2} + b^{2} = 0

On comparing with (i) we get,

a_{1 =} (a + b),

b_{1} = (a — b),

c_{1 =} – a^{2} – 2ab + b^{2};

a_{2} = (a – b),

b_{2} = (a – b),

c_{2} = – a^{2} + b^{2} = b^{2} – a^{2} = (b + a)(b – a) **{Using a ^{2} – b^{2} = (a + b)(a – b)}**

Applying cross multiplication method which says,

Putting the given values in the above equation we get,

Similarly,

∴The solution of the pair of equations is (a, b).

Rate this question :

Solve the following pair of linear equations by the method of cross – multiplication:

(a + b)x + (a — b)y = a^{2} + 2ab — b^{2}, a ≠ b

(a — b) (x + y) = a^{2} — b^{2}, a ≠ b

The sum of the digits of two–digit number is 3. The number obtained by interchanging the digits is 9 less than the original number. Find the original number.

Gujarat Board MathematicsThe sum of two numbers is 35. Four times the larger number is 5 more than 5 times the smaller number. Find these numbers.

Gujarat Board MathematicsSolve the following pair of linear equations by elimination method:

x + y = a + b, ax — by = a^{2} — b^{2}

In AABC, the measure of ∠B is thrice to the measure of ∠C and the measure of ∠A is the sum of the measures of ∠B and ∠C. Find the measures of all the angles of AABC and also state the type of this triangle.

Gujarat Board MathematicsSolve the following pairs of equations by cross multiplication method:

3x + y = 5, 5x + 3y = 3

Gujarat Board MathematicsSolve the following pairs of equations by cross multiplication method:

0.3x + 0.4y = 2.5 and 0.5x — 0.3y = 0.3

Gujarat Board MathematicsSolve the following pairs of equations by cross multiplication method:

, 7x— 15y = 21

Gujarat Board Mathematics