Solve each of the following systems of equations by the method of cross-multiplication:
2x – y = 6
x – y = 2
Answers
Concept :
CROSS - MULTIPLICATION METHOD:
The general form of a pair of linear equations
a1x + b1y + c1 = 0 , & a2x + b2y + c2 = 0.
When a1 / a2 ≠ b1 / b2, the pair of linear equations will have a unique solution.
To solve this pair of equations for x and y using cross-multiplication, we’ll arrange the variables x and y and their coefficients a1, a2, b1 and b2, and the constants c1 and c2 as shown below
⇒ x = b1 c2 - b2 c1 / a1 b2 - a2 b1
⇒ y = c1 a2 - c2 a1 / a1 b2 - a2 b1
The above equation is generally written as :
x/ b1 c2 - b2 c1 = y/ c1 a2 - c2 a1 = 1/a1 b2 - a2 b1
x y 1
----------- = ----------------- = ---------
b1 c1 c1 a1 a1 b1
b2 c2 c2 a2 a2 b2
Given :
2x - y = 6
x - y = 2
Solution :
We have ,
2x - y - 6 = 0
x - y - 2 = 0
Here a1 = 2, b1 = -1, c1 = - 6
a2 = 1, b2 = - 1, c2 = - 2
x y 1
----------- = ----------------- = ---------
-1 -6 - 6 2 2 - 1
-1 - 2 - 2 1 1 -1
x/(- 1 × - 2) - (- 1 × - 6) = y/(- 6 × 1) - (- 2 × 2) = 1/(2 × - 1) - (1 × -1)
x/ 2 - 6 = y/- 6 + 4 = 1/ - 2 + 1
x/- 4 = y/- 2 = 1/- 1
Now, x/- 4 = 1/- 1
x = 4
And
y/- 2 = 1/- 1
y = 2
Hence the value of given systems of equations is x = 4 and y = 2.
Hope this answer will help you…
Some more questions from this chapter :
Solve each of the following systems of equations by the method of cross-multiplication :
2x + y = 35
3x + 4y = 65
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Solve each of the following systems of equations by the method of cross-multiplication :
3x + 2y + 25 = 0
2x + y + 10 = 0
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Answer:
Cross multiply it to get your results try it yourself now. .....coz more you do practisce you become perfect