Question

Solve by elimination method 5x-2y=11, 3x+4y=4.​

Answer 1

x = 2 y= -1/2

Explanation:

5x-2y=11 {1} . 2

3x+4y=4 {2} . 1

-> 10x-4y=22

+ 3x+4y = 4

-> 13x = 26

-> x= 26/13 x= 2/1 x= 2

-> 3(2)+4y=4

->6+4y=4 -> 4y= 4-6

-> 4y= -2 -> y= -2/4 -> y=-1/2

Answer 2

★ How to do :-

Here, we are given with two equations. We are asked to find the value of x and y using substitution method. By using the first equation we will find the value of x by substituting the values. Then, we use the hint of x and then we can find the value of y. Then we can find the original value of x by using the value of y. Here, we also shift numbers from one hand side to the other which changes it's sign. So, let's solve!!

`\:`

➤ Solution :-

`{\sf \leadsto 5x - 2y = 11 \: --- (i)}`

`{\sf \leadsto 3x + 4y = 4 \: --- (ii)}`

First let's find the value of x by using first equation.

`{\tt \leadsto 5x - 2y = 11}`

Shift the number 2y from LHS to RHS, changing it's sign.

`{\tt \leadsto 5x = 11 - 2y}`

Shift the number 5 from LHS to RHS.

`{\tt \leadsto x = (11 - 2y)/(5)}`

`\:`

Now, let's find the value of y using the second equation.

Value of y :-

`{\tt \leadsto 3x + 4y = 4}`

Substitute the value of x.

`{\tt \leadsto 3 \bigg( (11 - 2y)/(5) \bigg) + 4y = 4}`

Multiply the number 3 with both numbers in brackets.

`{\tt \leadsto (33 - 6y)/(5) + 4y = 4}`

Convert the number 4y to like fraction and add it with the fraction.

`{\tt \leadsto (33 - 6y + 20y)/(5) = 4}`

Add the variable values on denominator.

`{\tt \leadsto (33 + 14y)/(5) = 4}`

Shift the number 5 from LHS to RHS.

`{\tt \leadsto 33 + 14y = 5 * 4}`

Multiply the values on RHS.

`{\tt \leadsto 33 + 14y = 20}`

Shift the number 33 from LHS to RHS, changing it's sign.

`{\tt \leadsto 14y = 20 - 33}`

Subtract the values on RHS.

`{\tt \leadsto 14y = (-13)}`

Shift the number 14 from LHS to RHS.

`{\tt \leadsto y = ((-13))/(14)}`

`\:`

Now, let's find the value of x by second equation.

Value of x :-

`{\tt \leadsto 3x + 4y = 4}`

Substitute the value of y.

`{\tt \leadsto 3x + 4 \bigg( ((-13))/(14) \bigg) = 4}`

Multiply the number 4 with the fraction in bracket.

`{\tt \leadsto 3x + ((-52))/(14) = 4}`

Shift the fraction on LHS to RHS, changing it's sign.

`{\tt \leadsto 3x = 4 - ((-52))/(14)}`

Convert the values on LHS to like fractions.

`{\tt \leadsto 3x = (56)/(14) - ((-52))/(14)}`

Subtract those fractions now.

`{\tt \leadsto 3x = (108)/(14)}`

Shift the number 3 from LHS to RHS.

`{\tt \leadsto x = (108)/(14) / (3)/(1)}`

Take the reciprocal of second fraction and multiply both fractions.

`{\tt \leadsto x = (108)/(14) * (1)/(3)}`

Write those fractions in lowest form by cancellation method.

`{\tt \leadsto x = \frac{\cancel{108}}{14} * \frac{1}{\cancel{3}} = (36 * 1)/(14 * 1)}`

Write the fraction in lowest form to get the answer.

`{\tt \leadsto x = \cancel (36)/(14) = (18)/(7)}`

`\:`

`{\red{\underline{\boxed{\bf So, \: the \: value \: of \: x \: and \: y \: is (18)/(7) \: and \: ((-13))/(14) \: respectively.}}}}`