Solve each of the following systems of equations by the method of cross-multiplication:
3x + 2y + 25 = 0
2x + y + 10 = 0
Answers
Answer:
x=5, y=-20
Step-by-step explanation:
Hope this will help you
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 :
3x + 2y + 25 = 0
2x + y + 10 = 0
Here a1 = 3, b1 = 2, c1 = 25
a2 = 2, b2 = 1, c2 = 10
x y 1
----------- = ----------------- = ---------
2 25 25 3 3 2
1 10 10 2 2 1
x/( 2 × 10) - (25 × 1) = y/(25 × 2) - (3 × 10) = 1/(3 × 1) - (2 × 2)
x/20 - 25 = y/50 - 30 = 1/ 3 - 4
x/- 5 = y/20 = 1/-1
Now, x/-5 = 1/-1
x = 5
And
y/20 = 1/-1
y = - 20
Hence the value of given systems of equations is x = 5 and y = - 20.
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 :
x + 2y + 1 = 0
2x - 3y - 12 = 0
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Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x+5y=9
3x+2y=4
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