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Solve the system of equations. 2x-4y=-4 and 2x-2y =0

Question:

Solve the system of equations.

{eq}2x - 4y = -4 {/eq} and {eq}2x - 2y = 0 {/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.

Answer and Explanation:

The given equations are:

$$\begin{align} 2 x - 4 y &= -4 &\rightarrow (1) \\ 2x- 2 y &= 0&\rightarrow (2) \end{align} $$

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

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

Now, add (2) and (3):

$$(2x-2y)+(-2x+4y)=0+4 \\[0.3cm] 2y=4 \\[0.3cm] \text{Dividing both sides by 2}, \\[0.3cm] y=2 $$

Substitute this in (1):

$$2x- 4 \left( 2\right)=-4 \\[0.3cm] 2x-8=-4 \\[0.3cm] \text{Adding 8 on both sides}, \\[0.3cm] 2x=4 \\[0.3cm] \text{Dividing both sides by 2}, \\[0.3cm] x= 2 $$

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


Learn more about this topic:

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Elimination Method in Algebra: Definition & Examples

from High School Algebra II: Help and Review

Chapter 7 / Lesson 9
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