Algebraic Manipulation Worksheets With Answers - Craven Community College (Page 22 of 29) in pdf

Algebraic Manipulation Worksheets With Answers - Craven Community College Page 22

Example:

X + 2Y = 4

2X + Y = -1

Check:

-2 + 2(3) = 4

2(-2) + 3 = -1

Thus X = -2 and Y = 3 is the solution to this system.

If the lines are parallel, there is no solution to the system. These systems are called inconsistent. If both

equations produce the same line, there are infinitely many solutions to the system. These systems are

called dependent.

Solving Systems of Equations by Elimination

A common algebraic method of solving systems of equations is the Elimination Method. In this method,

each equation is first multiplied by a non-zero number so that the sum of the coefficients on either X or

Y is zero. The equations are then added together producing a new equation in one variable. This equation

is solved, and the solution substituted back into one of the original equations to obtain the solution value

of the other variable.

Example:

2X – 5Y = 1

3X – 4Y = 5

Multiply the first equation by -3 and the second by 2 so that the sum of the coefficients on the X

variable will be zero.

-3[2X – 5Y = 1]

-6X + 15Y = -3

2[3X – 4Y = 5]

6X – 8Y = 10

Add equations

7Y = 7

Divide by 7

Y = l

Algebraic Manipulation Worksheets With Answers - Craven Community College Page 22