Solve the system of equation. 2x+3y=1 4x+6y=2

Question:

Solve the system of equation.

{eq}2x + 3y = 1 {/eq}

{eq}4x + 6y = 2 {/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 equations are:

\begin{align} 2x+3y&=1 & \rightarrow (1) \\ 4x+6y&=2 & \rightarrow (2) \end{align}

We will solve this system using the elimination method.

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

$$-4x-6y=-2\,\,\,\,\,\,\,\ \rightarrow (3)$$

$$(4x+6y) +(-4x-6y) = 2+(-2) \\ \text{Combining the like terms}, \\ 0=0$$

The above equation is without variables and is TRUE forever.

Therefore, the given system has INFINITELY MANY SOLUTIONS.