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Chapter 4: Problem 73
When using the addition method, how can you tell if a system of linear equations has infinitely many solutions?
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In Exercises \(61-68,\) solve each system or state that the system is inconsistent or dependent. $$\left\\{\begin{array}{l} \frac{x}{2}=\frac{y+8}{3} \\ \frac{x+2}{2}=\frac{y+11}{3} \end{array}\right.$$
When using the addition method, how can you tell if a system of linear equations has no solution?
In Exercises \(45-56,\) solve each system by the method of your choice. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. Explain why you selected one method over the other two. $$\left\\{\begin{aligned} 3 x-2 y &=8 \\ x &=-2 y \end{aligned}\right.$$
In Exercises \(45-56,\) solve each system by the method of your choice. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. Explain why you selected one method over the other two. $$\left\\{\begin{array}{l} 2 x-7 y=17 \\ 4 x-5 y=25 \end{array}\right.$$
The law of supply and demand states that, in a free markes economy, a commodity tends to be sold at its equilibriunprice. At this price, the amount that the seller will supply is the same amount that the consumer will buy. Explair how systems of equations can be used to determine the equilibrium price.
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