Solve using the elimination method: -4x + 9y = 9 x - 3y = -6

Question:

Solve using the elimination method:

{eq}-4x + 9y = 9 \\ \ \ x - 3y = -6 {/eq}

Solution of the Linear Equations:

{eq}\\ {/eq}

The solution or the set of values of {eq}x {/eq} and {eq}y {/eq} for the given set of linear equations will be determined using the method of elimination. In this method, we eliminate one of the variables out of {eq}x {/eq} and {eq}y {/eq} using some scalar multiplication and basic arithmetic operations. Once we have the value of one variable, we can evaluate the value of other variables using any of the given equations.

Answer and Explanation:

{eq}\\ {/eq}

{eq}-4x + 9y = 9 \; \; \cdots \cdots \; \; (1) \\ x - 3y = - 6 \; \; \cdots \cdots \; \; (2) {/eq}

Now multiply equation (2) with a scalar of {eq}4 {/eq} in order to make the coefficients of {eq}x {/eq} equal but of opposite sign in both the equations:

{eq}4 (x - 3y) 4 \times (-6) \\ 4x - 12y = -24 \; \; \cdots \cdots \; \; (3) {/eq}

Now add equation (1) and equation (3) in order to eliminate the variable {eq}x {/eq}:

{eq}9y - 12y = 9 - 24 \\ -3y = -15 \\ \Longrightarrow y = \dfrac {15}{3} = 5 {/eq}

Now put the value of {eq}y = 5 {/eq} in equation (1) in order to get the value of {eq}x {/eq}:

{eq}-4x + 9 \times 5 = 9 \\ -4x = 9 - 45 \\ -4x = - 36 \\ \Longrightarrow x = \dfrac {36}{4} = 9 {/eq}

Finally, we have the values of the variables {eq}x {/eq} and {eq}y {/eq} given below:

{eq}\Longrightarrow \boxed {(x, \; y) = (9, \; 5)} {/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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