91Ó°ÊÓ

Solve each system of equations by the addition method. See Example 1 $$ \left\\{\begin{array}{l} {3 x+y=5} \\ {6 x-y=4} \end{array}\right. $$

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} {x+y=3} \\ {x=2 y} \end{array}\right. $$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}{x+y=8} \\ {3 x+2 y=21}\end{array}\right.\) a. \((2,4)\) b. \((5,3)\)

Solve. Choose the equation(s) that has \((-1,3,1)\) as a solution. $$A. x+y+z=3$$ $$B. -x+y+z=5$$ $$C. -x+y+2 z=0$$ $$D. x+2 y-3 z=2$$

Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions. The length of a rectangle is 3 feet longer than the width. The perimeter is 30 feet. Find the dimensions of the rectangle. a. length \(=8\) feet; width \(=5\) feet b. length \(=8\) feet; width \(=7\) feet c. length \(=9\) feet; width \(=6\) feet

Solve. Choose the equation (s) that has \((2,1,-4)\) as a solution. $$A. x+y+z=-1$$ $$B. x-y-z=-3$$ $$C. 2 x-y+z=-1$$ $$D. -x-3 y-z=-1$$

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and \(2 .\) \(\left\\{\begin{array}{l}{2 x+y=5} \\ {x+3 y=5}\end{array}\right.\) a. \((5,0)\) b. \((2,1)\)

Solve each system of equations by the addition method. See Example 1 $$ \left\\{\begin{array}{l} {4 x+y=13} \\ {2 x-y=5} \end{array}\right. $$

Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions. An isosceles triangle, a triangle with two sides of equal length, has a perimeter of 20 inches. Each of the equal sides is one inch longer than the third side. Find the lengths of the three sides. a. 6 inches, 6 inches, and 7 inches b. 7 inches, 7 inches, and 6 inches c. 6 inches, 7 inches, and 8 inches

Solve each system of equations by the substitution method. $$ \left\\{\begin{array}{l} {x+y=20} \\ {x=3 y} \end{array}\right. $$