7. Systems of Equations & Matrices

In Exercises 19–30, solve each system by the addition method.3x - 4y = 112x + 3y = - 4

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2.x/2+ y/3 = 43x/2+3y/2 = 15

Solve each system by elimination. In systems with fractions, first clear denominators. See Example 2.(2x-1)/3 + (y+2)/4 = 4(x+3)/2 - (x-y)/2 = 3

In Exercises 19–30, solve each system by the addition method.3x = 4y + 13y = 1 - 4x

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x = 9-2yx + 2y = 13

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary. See Examples 3 and 4.9x - 5y = 1 -18x + 10y = 1

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. y = 3x - 521x - 35 = 7y

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3x - 2y = − 54x + y = 8

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x + 3y = 23x + 9y = 6

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. x/4 - y/4 = −1x + 4y = -9

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 2x = 3y + 44x = 3 - 5y

Determine the system of equations illustrated in each graph. Write equations in standard form.

Determine the system of equations illustrated in each graph. Write equations in standard form.

In Exercises 43–46, let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3(x + y)/5 = (x - y)/2 - 5/2