Solve each of the following systems of equations by the method of cross-multiplication:
x + 2y + 1 = 0
2x – 3y – 12 = 0
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 : x + 2y + 1 = 0
2x – 3y – 12 = 0
Solution :
Here a1 = 1, b1 = 2, c1 = 1
a2 = 2, b2 = - 3, c2 = – 12
x y 1
----------- = ----------------- = ---------
2 1 1 1 1 2
-3 -12 -12 2 2 -3
X/ 2 × - 12 - (-3 × 1) = y/2 × 1 - (- 12 × 1) = 1/(1 × - 3) - (2 × 2)
X/- 24 + 3 = y/2 + 12 = 1/-3 - 4
X/-21 = y/14 = 1/-7
Now, X/-21 = 1/-7
-7x = - 21
x = 21/7
x = 3
And
y/14 = 1/-7
-7y = 14
y = -14/7
y = - 2
Hence the value of given systems of equations is x = 3 and y = - 2.
Hope this answer will help you…
Some more questions from this chapter :
Solve by Cross Multiplication method :x /a +y / b= a + b , x/ a² + y/b²= 2.
https://brainly.in/question/2810989
Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x+5y=9
3x+2y=4
https://brainly.in/question/1345030
x = 3, y = -2
Step-by-step explanation:
Given linear equations are:
x + 2y + 1 = 0
2x – 3y – 12 = 0
We get:
x + 2y = -1 -------------(1)
2x - 3y = 12 -------------(2)
(1)*3 will be 3x + 6y = -3
(2)* 2 will be 4x - 6y = 24
Adding both, we get: 7x = 21
Therefore x = 3
Substituting x=3 in equation 1, we get 3 + 2y = -1
2y = -4
Therefore y = -2.
Hence solved. x = 3, y = -2