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Solve the system of equations: c - 3 d = 27 4 d + 10 c = 120.

Question:

Solve the system of equations:

{eq}c - 3 d = 27\\ 4 d + 10 c = 120. {/eq}

System of equation:

The system of equation can be defined as the collection which is used to determine the values of the variables with the help of basic operation of mathematics and substitution method.

Answer and Explanation:


Write the system of equations.

{eq}\begin{align*} c - 3d &= 27.....................(I)\\ 4d + 10c &= 120.................(II) \end{align*} {/eq}


Multiply with {eq}4 {/eq} in equation (I) and {eq}3 {/eq} in equation (II) and add both the equations.

{eq}\begin{align*} 4c - 12d + 12d + 30c &= 108 + 360\\ 34c &= 468\\ c &= \frac{{468}}{{34}}\\ &= \frac{{234}}{{17}}\\ &= 13.764 \end{align*} {/eq}


Substitute 13.764 for c equation (I).

{eq}\begin{align*} 13.764 - 3d &= 27\\ 13.764 - 27 &= 3d\\ d &= \frac{{ - 13.236}}{3}\\ &= - 4.412 \end{align*} {/eq}


Thus, the value for c and d respectively is {eq}13.764 {/eq} and {eq}- 4.412 {/eq}.


Learn more about this topic:

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Inconsistent System of Equations: Definition & Example

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 9
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