Question

Solve 2x + 5y = 1 and 2x-y=7?​

Answer 1

ANSWER:

TO SOLVE:

• 2x + 5y = 1
• 2x - y = 7

SOLUTION:

There are many methods of solving pair of linear equations. The most common are substitution method and elimination method.

Method 1: Substitution Method

⇒ 2x + 5y = 1 -----(1)

⇒ 2x - y = 7

⇒ y = 2x - 7 ----(2)

Putting (2) in (1),

⇒ 2x + 5(2x - 7) = 1

⇒ 2x + 10x - 35 = 1

⇒ 12x = 36

⇒ x = 3

⇒ y = 2x - 7 = 2*3 - 7 = 6 - 7 = -1

So,

⇒ x = 3 and y = -1

Method 2: Elimination Method

⇒ 2x + 5y = 1 -----(3)

⇒ 2x - y = 7 -----(4)

As the coefficient of x in both the equations is same, hence we eliminate x.

Subtracting (4) from (3),

⇒ (2x + 5y) - (2x - y)= (1) - (7)

⇒ 2x + 5y - 2x + y = 1 - 7

⇒ 6y = -6

⇒ y = -1

Putting value of y in (4),

⇒ 2x - (-1) = 7

⇒ 2x + 1 = 7

⇒ 2x = 7 - 1

⇒ 2x = 6

⇒ x = 3

So,

⇒ x = 3 and y = -1

LEARN MORE:

• In substitution method, we calculate one variable in terms of the other and substitute it in the other equation.
• In elimination method, we eliminate one variable by either adding or subtracting the equations and then putting that value in one of the equation to get value of the other variable.

Answer 2

Answer:

x= 1

y = 2

And

x = 2

y=11

.

.

॥