Solve 11x + 15y + 23 = 0, 7x - 2y - 20 = 0 by elimination method.

By Ritesh|Updated : November 7th, 2022

Solving 11x + 15y + 23 = 0, 7x - 2y - 20 = 0 by elimination method we get x = 2 and y = -3. When one or both equations are multiplied by factors, only one variable remains after adding or subtracting the resulting two equations. One method for resolving a system of linear equations is the elimination method. In this approach, the equation in one variable is obtained by either adding or subtracting the equations. We can add the equation to delete a variable if its coefficients are the same and have the opposite sign from the other variables. Similarly to this, we can subtract the equation to get the equation in one variable if the coefficients of one of the variables are the same and their signs are the same.

You can start by multiplying one or both equations by a constant value on both sides of an equation to obtain the equivalent linear system of equations, and then eliminate the variable by simply adding or subtracting equations if we do not have the equation to directly add or subtract the equations to do so.

Steps to Solve the Equation by Elimination Method

Given: 11x + 15y + 23 = 0, 7x - 2y - 20 = 0

When the first equation is multiplied by 2 and the second equation by 15, we obtain

2 x (11x + 15y + 23) = 0

22x + 30y + 46 = 0 …… (1)

15 x (7x - 2y - 20) = 0

105x - 30y - 300 = 0 …. (2)

adding both equations, we get

22x + 30y + 46 + 105x - 30y - 300 = 0

127x - 254 = 0

127x = 254

On simplifying we get

x = 254/127

x = 2

Put the value of x in equation (1) we get

22x + 30y + 46 = 0

22 (2) + 30y + 46 = 0

44 + 30y + 46 = 0

30y + 90 = 0

30y = -90

On simplifying we get

y = -90/30

y = -3

Consequently, x and Y have values of 2 and -3.

Summary:

Solve 11x + 15y + 23 = 0, 7x - 2y - 20 = 0 by elimination method.

Solving 11x + 15y + 23 = 0, 7x - 2y - 20 = 0 by elimination method we get x = 2 and y = -3. In this method, the equation present in one variable is got by either addition or subtraction of the equations.

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