Question

# Solve the system of equations by elimination :

4Y + 2X = - 7

2Y - 6x = 8

Hint:

**HINT:** Perform any arithmetic operation and then find.

## The correct answer is: x=-23/14 and y=(-13)/14

### Complete step by step solution:

Let 4y + 2x = - 7…(i)

and 2y - 6x = 8….(ii)

On multiplying (ii) with 2, we get 2(2y - 6x = 8)

⇒4y - 12x = 16…(iii)

Now, we have the coefficients of y in (i) and (iii) to be the same.

On subtracting (i) from (iii),

we get LHS to be 4y - 12x-(4y + 2x) = - 12x - 2x = - 14x

and RHS to be 16 - ( - 7) = 23

On equating LHS and RHS, we have - 14 x = 23

On substituting the value of x in (i), we get

Hence we get

Note: We can also solve these system of equations by making the coefficients of x

to be the same in both the equations.

Hence we get

Note: We can also solve these system of equations by making the coefficients of x

to be the same in both the equations.

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Finding the answer to the given linear equation is the act of solving a linear equation. One of the algebraic techniques for solving a system of two-variable linear equations is the substitution approach. As the name suggests, the replacement method involves substituting a variable's value into a second equation. As a result, two linear equations are combined into one linear equation with just one variable, making it simple to solve. As an illustration, let us swap the value of the x-variable from the second equation and the y-variable from the first equation. By solving the problem, we can determine the value of the y-variable. Last but not least, we can solve any of the preceding equations by substituting the value of y. This procedure can easily be switched around so that we first solve for x before moving on to solve for y.