## Consistent System of Equations:

When it comes to linear equations there are two instances when a system of linear equations are consistent. It is when the lines intersect each other at a unique point and when the lines are coincident.

The club earns 1,360 selling 45 adult meals and 80 student meals. Let {eq}x {/eq} stand for the cost of a student meal and {eq}2x {/eq} for the cost of an adult meal. The equation for the amount involved for all the meals would be: {eq}80x + 45(2x) = 1360 {/eq} Solving for {eq}x {/eq}: {eq}\begin{align} 80x + 45(2x) &= 1360 \\ 80x + 90x &= 1360 \\ 170x &= 1360 \\ \dfrac {170x}{170} &= \dfrac{1360}{170} \\ x &= 8 \end{align} {/eq} Since the adult meal is twice the amount of the student meal: {eq}2x = 2(8) = 16 {/eq} The cost of an adult meal is16.00.

Consistent System of Equations: Definition & Examples

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 8
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