# Solve the system of equations: 2 x - 4 y = 7 4 x + 2 y = 9.

## Question:

Solve the system of equations:

{eq}2 x - 4 y = 7 \\ 4 x + 2 y = 9. {/eq}

## Elimination Method:

(i) The elimination method is used to solve a system of two equations in two variables.

(ii) In this method, we add or subtract the given equations and eliminate one variable.

(iii) We solve the resultant equation in one variable using the algebraic operations.

The given equations are:

\begin{align} 2 x - 4 y &= 7 &\rightarrow (1) \\ 4 x + 2 y &= 9&\rightarrow (2) \end{align}

Multiply both sides of (1) by {eq}-2 {/eq},

$$-4x+8y=-14 \,\,\,\,\,\,\,\rightarrow (3)$$

$$(4x+2y)+(-4x+8y)=9+(-14) \\[0.3cm] 10y=-5 \\[0.3cm] \text{Dividing both sides by 10}, \\[0.3cm] y= \dfrac{-5}{10}= \dfrac{-1}{2}$$

Substitute this in (1):

$$2x- 4 \left( \dfrac{-1}{2}\right)=7 \\[0.3cm] 2x+2=7 \\[0.3cm] \text{Subtracting 2 from both sides}, \\[0.3cm] 2x=5 \\[0.3cm] \text{Dividing both sides by 2}, \\[0.3cm] x= \dfrac{5}{2}$$

Therefore, the solution is, {eq}\boxed{\mathbf{x=\dfrac{5}{2} \text { and } y=-\dfrac{1}{2}}} {/eq}