Question
Solve the system of equations by elimination :
7X - 4Y = - 12
X - 2Y = 4
Hint:
Perform any arithmetic operation and then find.
The correct answer is: We can also solve these system of equations by making the coefficients of y to be the same in both the equations.
Complete step by step solution:
Let 7x - 4y = - 12…(i)
and x - 2y = 4….(ii)
On multiplying (ii) with 7, we get 7( x - 2y = 4)
⇒ 7x - 14y = 28…(iii)
Now, we have the coefficients of x in (i) and (iii) to be the same.
On subtracting (i) from (iii),
we get LHS to be 7x - 14y - (7x - 4y) = - 14y + 4y = - 10y
and RHS to be 28 -( - 12 = 40
On equating LHS and RHS, we have - 10y=40
⇒ y = - 4
On substituting the value of in (i), we get 7x - 4× - 4 = - 12
⇒ 7x + 16 = - 12
⇒ 7x = - 12 - 16
⇒ 7x = - 28
⇒x = - 4
Hence we get x = - 4 and y = - 4
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations.
Related Questions to study
Richard and teo have a combined age of 31 . Richard is 4 years older than twice teo's age. How old are Richard and teo?
Tips to help you answer the questions on the problems of age: a.) The age after n years will be (x+n) if you assume that the current age is x.
b.) The age before n years will be (x-n) if you assume the present age to be x.
c.) If the age is expressed as a ratio, p:q, the age will be rounded to the nearest multiple of q and p.
d.) Given that you are assuming you are currently x years old, n times that number equals (xn) years.
E.g.:The father is three times older than Ronit. So he would be 2.5 times Ronit's age after '8' years. How many more times would he be Ronit's age after another '8' years?
A. 2 times
B. 2 1/2 times
C. 2 3/4 times
D. 3 times
Richard and teo have a combined age of 31 . Richard is 4 years older than twice teo's age. How old are Richard and teo?
Tips to help you answer the questions on the problems of age: a.) The age after n years will be (x+n) if you assume that the current age is x.
b.) The age before n years will be (x-n) if you assume the present age to be x.
c.) If the age is expressed as a ratio, p:q, the age will be rounded to the nearest multiple of q and p.
d.) Given that you are assuming you are currently x years old, n times that number equals (xn) years.
E.g.:The father is three times older than Ronit. So he would be 2.5 times Ronit's age after '8' years. How many more times would he be Ronit's age after another '8' years?
A. 2 times
B. 2 1/2 times
C. 2 3/4 times
D. 3 times
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