Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 14.6 Solve Systems by Multiplying to Make an Equivalent Equation
Document related concepts
Transcript
14.6 Solve Systems by Multiplying to Make an Equivalent Equation Common Core Standards 8. EE. 8 Analyze and Solve pairs of Simultaneous Equations a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. WARM-UP Solve the system of linear equations by elimination. 3x + 2y = 18 4x − 2y = −4 y 8 6 4 2 -8 -6 -4 -2 0 -2 -4 -6 -8 x 2 4 6 8 Solve Systems by Multiplying to Make an Equivalent Equation How do we use the elimination method when there aren't terms that are the same or opposite? 3x + y = 13 6x − 4 y = 2 NOTES When there aren't terms that are the same or opposite, multiply both sides of one equation to create terms that can be eliminated. Examples Solve the system of equations. 2x + 3y = 15 x + 4y = 10 EXAMPLES Solve the system of equations. x − 2y = 1 3x + 4y = 23 4x − y = 4 3x + 3y = 18 EXAMPLES Solve the system of equations. 2x + 3y = 15 −6x + 2y = −12 NOTES (x, y) coordinates can contain fractions. Examples Solve the system of equations. x − 2y = 0 3x + 4y = −2 NOTES If the lines are parallel, there will be no solution. Examples Solve the system of equations. x + 2y = 6 2x + 4y = −4 y 8 6 4 2 -8 -6 -4 -2 0 -2 -4 -6 -8 x 2 4 6 8 PRACTICE Solve the system of equations by elimination. 4x − 3y = −17 x + 2y = 4 −5x + 2y = 12 2x − 6y = 3 FINAL QUESTION Solve the system of equations. 3x − y = 10 9x − 3y = 4
