University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

304

Pages:

3
Author:

Enriquearrimadeo2

Review Solving 1 & 2 Equations Pre-Calculus One-sided variable 3x + 6 = 30 -6 -6 3x/3 = 24/3 x = 8 6x - 3 = 15 +3 +3 6x/6 = 18/6 x = 3 -6 + 4x = 34 +6 +6 4x/4 = 40/4 x = 10 5x + 4 = -41 -4 -4 5x/5 = -45/5 x = -9 108 = -5x - 7 +7 +7 115/-5 = -5x/-5 -23 = x -18 - 6x = -132 +18 +18 -6x/-6 = -114/-6 x = 19 5(3x - 2) = 35 3x - 2 = 7 +2 +2 3x/3 = 9/3 x = 3 -3(4 + 3x) = 27 4 + 3x = -9 -4 -4 3x/3 = -13/3 x = -13/3 2(3 + 4x) - 9 = 45 6 + 8x - 9 = 45 8x - 3 = 45 +3 +3 8x/8 = 48/8 x = 6 6x - 4(2x + 8) = 16 6x - 8x - 32 = 16 -2x - 32 = 16 +32 +32 -2x/-2 = 48/-2 x = -24 -5x + 4(2 + 2x) = -1 -5x + 8 + 8x = -1 3x + 8 = -1 -8 -8 3x/3 = -9/3 x = -3 Variables on both sides 4x - 7 = 3x +7 +7 x = 7 2x - 1 = 4 + x -x -x x - 1 = 4 +1 +1 x = 5 5 - 3x = 2x - 8x + 40 5 - 3x = -6x + 40 +6x +6x 5 + 3x = 40 -5 -5 3x/3 = 35/3 x = 35/3 4(x + 2) - 21 = 2 + 3(x - 6) 4x + 8 - 21 = 2 + 3x - 18 4x - 13 = 3x - 16 -3x -3x x - 13 = -16 +13 +13 x = -3 13 - 1(2x + 2) = 2(x + 2) + 3x 13 - 2x - 2 = 2x + 4 + 3x 11 - 2x = 5x + 4 -5x -5x 11 - 7x = 4 -11 -11 -7x/-7 = -7/-7 x = 1 Solve 2 equations There are two ways to solve two equations 2y - 5x = 11 y = 2x + 7 Substitution Method Use x or y for one equation... make it happen y = 2x + 7 Plug that into the second equation. 2(2x + 7) - 5x = 11 Solve for the remaining variable 2(2x + 7) - 5x = 11 4x + 14 - 5x = 11 -x = -3 x = 3 Go back and find the other variable in the first equation. y = 2(3) + 7 y = 6 + 7 y = 13 Double Check the answers in the second equation. 2(13) - 5(3) = 11 26 - 15 = 11 11 = 11 Guarantee that the answers are correct If it doesn't check, go back and find your error What if you get..... 0 = 0 2 = 2 -7 = -7 indication of infinite # of Solutions 2y - 5x = 11 y = 2x + 7 Elimination (Addition) Method Line up the equations so you can eliminate a variable 2y - 5x = 11 y = 2x + 7 -> (y - 2x = 7) 2y - 5x = 11 -2y + 4x = -14 -x = -3 Solve for the remaining variable -x = -3 x = 3 Find the other variable by plugging it into one equation. 2y - 5(3) = 11 2y - 15 = 11 +15 +15 2y/2 = 26/2 y = 13 Double Check answers in the other equation. 13 = 2(3) + 7 13 = 6 + 7 13 = 13 Guarantee that the answers are correct If it doesn't check, go back and find your error What if you get..... 0 = 13 2 = -2 9 = 5 indication of No Solution Now you practice. 17) 3y - x = 5 y = 2x - 5 3(2x - 5) - x = 5 6x - 15 - x = 5 5x - 15 = 5 5x = 20 x = 4 y = 2(4) - 5 y = 8 - 5 y = 3 3(3) - (4) = 5 9 - 4 = 5 5 = 5 18) 2y + 3x = 4 -1y - 6x = -2 2y + 3x = 4 -2y - 12x = -4 0 = 0 Infinite # of Solutions 19) 3x + 2y = 17 9x + 6y = 51 3x + 2y = 17 -3x - 2y = -17 0 = 0 20) 3x + 5y = -2 2x + 3y = -1 -6x - 10y = 4 6x + 9y = -3 -y = 1 y = -1 3x + 5(-1) = -2 3x - 5 = -2 3x = 3 x = 1 2(1) + 3(-1) = -1 2 - 3 = -1 -1 = -1 21) 4x - 5y = 7 5y = 4x + 7 4x - 5y = 7 -4x + 5y = 7 0 = 14 No Solution 22) x + y = -5 3y - x = 9 y + x = -5 3y - x = 9 4y = 4 y = 1 x + (1) = -5 x = -6 3(1) - (-6) = 9 3 + 6 = 9 9 = 9