# Solve the system of equations by using the elimination method. 4x +5y=5 and 8x +10y=10

## Question:

Solve the system of equations by using the elimination method.

{eq}4x + 5y = 5 {/eq} and {eq}8x + 10y = 10 {/eq}

## Elimination Method:

A system of two equations can be solved in many methods. One of the methods is the "elimination method". In this method, we add or subtract the equations to get a variable canceled. We will solve the resultant equation for the other variable.

• If this process leads to an equation without variables that is true then we say that the system has infinitely many solutions.
• If this process leads to an equation without variables that is false then we say that the system has no solution.

The given two equations are:

\begin{align} 4x +5y&=5 & \rightarrow (1) \\[0.4cm] 8x + 10y &= 10& \rightarrow (2) \end{align}

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

$$-2(4x +5y=5 ) \Rightarrow -8x-10y=-10 \,\,\,\,\,\,\,\,\,\rightarrow (3)$$

\begin{align} (-8x-10y)+(8x+10y) &= -10+10 \\ 0&=0 \end{align}

This equation is without variables and is TRUE forever.

Therefore, the given system has infinitely MANY solutions. 