Copyright

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.

Answer and Explanation:

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}:

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

Adding (1) and (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.


Learn more about this topic:

Loading...
Elimination Method in Algebra: Definition & Examples

from High School Algebra II: Help and Review

Chapter 7 / Lesson 9
23K

Related to this Question

Explore our homework questions and answers library