1. Solve linear equations x+y=2 and 2x+3y=4 using Cross Multiplication Method
Solution:
`x+y=2`
and `2x+3y=4`
`x+y-2=0 ->(1)`
`2x+3y-4=0 ->(2)`
Here,
`a_1=1, b_1=1, c_1=-2`
`a_2=2, b_2=3, c_2=-4`
`x=(b_1*c_2-b_2*c_1)/(a_1*b_2-a_2*b_1)`
`=((1)(-4)-(3)(-2))/((1)(3)-(2)(1))`
`=((-4)-(-6))/((3)-(2))`
`=(2)/(1)`
`=2`
`y=(c_1*a_2-c_2*a_1)/(a_1*b_2-a_2*b_1)`
`=((-2)(2)-(-4)(1))/((1)(3)-(2)(1))`
`=((-4)-(-4))/((3)-(2))`
`=(0)/(1)`
`=0`
`:.x=2" and "y=0`
2. Solve linear equations 2x+7y-11=0 and 3x-y-5=0 using Cross Multiplication Method
Solution:
`2x+7y-11=0`
`:.2x+7y=11`
and `3x-y-5=0`
`:.3x-y=5`
`2x+7y-11=0 ->(1)`
`3x-y-5=0 ->(2)`
Here,
`a_1=2, b_1=7, c_1=-11`
`a_2=3, b_2=-1, c_2=-5`
`x=(b_1*c_2-b_2*c_1)/(a_1*b_2-a_2*b_1)`
`=((7)(-5)-(-1)(-11))/((2)(-1)-(3)(7))`
`=((-35)-(11))/((-2)-(21))`
`=(-46)/(-23)`
`=2`
`y=(c_1*a_2-c_2*a_1)/(a_1*b_2-a_2*b_1)`
`=((-11)(3)-(-5)(2))/((2)(-1)-(3)(7))`
`=((-33)-(-10))/((-2)-(21))`
`=(-23)/(-23)`
`=1`
`:.x=2" and "y=1`
3. Solve linear equations 3x-y=3 and 7x+2y=20 using Cross Multiplication Method
Solution:
`3x-y=3`
and `7x+2y=20`
`3x-y-3=0 ->(1)`
`7x+2y-20=0 ->(2)`
Here,
`a_1=3, b_1=-1, c_1=-3`
`a_2=7, b_2=2, c_2=-20`
`x=(b_1*c_2-b_2*c_1)/(a_1*b_2-a_2*b_1)`
`=((-1)(-20)-(2)(-3))/((3)(2)-(7)(-1))`
`=((20)-(-6))/((6)-(-7))`
`=(26)/(13)`
`=2`
`y=(c_1*a_2-c_2*a_1)/(a_1*b_2-a_2*b_1)`
`=((-3)(7)-(-20)(3))/((3)(2)-(7)(-1))`
`=((-21)-(-60))/((6)-(-7))`
`=(39)/(13)`
`=3`
`:.x=2" and "y=3`
4. Solve linear equations 2x-y=11 and 5x+4y=1 using Cross Multiplication Method
Solution:
`2x-y=11`
and `5x+4y=1`
`2x-y-11=0 ->(1)`
`5x+4y-1=0 ->(2)`
Here,
`a_1=2, b_1=-1, c_1=-11`
`a_2=5, b_2=4, c_2=-1`
`x=(b_1*c_2-b_2*c_1)/(a_1*b_2-a_2*b_1)`
`=((-1)(-1)-(4)(-11))/((2)(4)-(5)(-1))`
`=((1)-(-44))/((8)-(-5))`
`=(45)/(13)`
`=45/13`
`y=(c_1*a_2-c_2*a_1)/(a_1*b_2-a_2*b_1)`
`=((-11)(5)-(-1)(2))/((2)(4)-(5)(-1))`
`=((-55)-(-2))/((8)-(-5))`
`=(-53)/(13)`
`=-53/13`
`:.x=45/13" and "y=-53/13`
This material is intended as a summary. Use your textbook for detail explanation.
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