University:
Bradley University
Course:
MTH 109 | College Algebra
Academic year:

2024
Views:

337

Pages:

1
Author:

Angelica Rose

6\VWHPVRI(TXDWLRQV³4XLFN5HIHUHQFH Two linear equations form a system of equations. You can solve a system of equations using one of three methods: 1. Graphing 2. Substitution Method 3. Linear Combinations Method Substitution Method Solve the following system of equations: x – 2y = -10 y= 3x x – 2y = -10 Since we know y = 3x, substitute 3x for y into x – 2(3x) = -10 the first equation. x – 6x = -10 Simplify: Multiply 2(3x) = 6x. -5x = -10 Simplify: x – 6x = -5x -5x = -10 -5 -5 Solve for x by dividing both sides by -5. x= 2 The x coordinate is 2. y = 3x y = 3(2) y=6 Since we know that x = 2, we can substitute 2 for x into y = 3x. Solution: (2, 6) The solution! Graphing Systems of Equations Linear Combinations (Addition Method) Solve the following system of equations: 3x+2y = 10 2x +5y = 3 The solution to a system of equations is the point of intersection. The ordered pair that is the point of intersection represents the solution that satisfies BOTH equations. If two lines are parallel to each other, then there is no solution. The lines will never intersect. If two lines lay one on top of another then there are infinite solutions. Every point on the line is a solution. Copyright © 2009 Algebra-class.com -2(3x + 2y = 10) 3(2x + 5y = 3) Create opposite terms. I’m creating opposite x terms. -6x – 4y = -20 6x + 15 y = 9 11y = -11 Multiply to create opposite terms. Then add the like terms. 11y = -11 11 11 Solve for y by dividing both sides by 11. y = -1 The y coordinate is -1 2x + 5y = 3 2x +5(-1) = 3 Substitute -1 for y into one of the equations. 2x – 5 = 3 2x -5 + 5 = 3 + 5 2x = 8 2 2 Solve for x! The solution (4, -1) x=4