91Ó°ÊÓ

In Exercises 41 and 42 , solve the system to find the two numbers. The sum of two numbers \(x\) and \(y\) is 82 and the difference of the numbers is 14 . The systems of equations that represents this problem is $$ \left\\{\begin{array}{l} x+y=82 \\ x-y=14 \end{array}\right. \text {. } $$

In Exercises \(41-46\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{aligned} x+y & \leq 4 \\ x & \geq 0 \\ y & \geq 0 \end{aligned}\right. $$

In Exercises 39-42, find \(m\) and \(b\) such that \(y=m x+b\) is the equation of the line through the points. $$ (-3,6),(5,2) $$

In Exercises 41 and 42 , solve the system to find the two numbers. The sum of two numbers \(x\) and \(y\) is 154 and the difference of the numbers is 38 . The system of equations that represents this problem is $$ \left\\{\begin{array}{l} x+y=154 \\ x-y=38 \end{array}\right. \text {. } $$

What is one of the drawbacks to solving a system of linear equations by graphing?

In Exercises 35-46, solve the system by the method of substitution. $$ \left\\{\begin{aligned} -\frac{x}{5}+\frac{y}{2} &=-3 \\ \frac{x}{4}-\frac{y}{4} &=0 \end{aligned}\right. $$

In Exercises \(41-46\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{r} 2 x+y \leq 6 \\ x \geq 0 \\ y \geq 0 \end{array}\right. $$

In Exercises 39-42, find \(m\) and \(b\) such that \(y=m x+b\) is the equation of the line through the points. $$ (0,2),(4,-8) $$

In Exercises \(43-48\), write the equations of the lines in slope-intercept form. What can you conclude about the number of solutions of the system? $$ \left\\{\begin{array}{r} 2 x-3 y=-12 \\ -8 x+12 y=-12 \end{array}\right. $$

In Exercises 35-46, solve the system by the method of substitution. $$ \left\\{\begin{array}{l} \frac{x}{4}+\frac{y}{2}=1 \\ \frac{x}{2}-\frac{y}{3}=1 \end{array}\right. $$