SOLUTION: solving systems of linear equations.solve by substitution 2x+y=10 3x-4y=26 y=2x+3 3x+2y=6 solving systems of linear equations.solve by addition elimination 3x-6y=5 2

Algebra ->  Expressions-with-variables -> SOLUTION: solving systems of linear equations.solve by substitution 2x+y=10 3x-4y=26 y=2x+3 3x+2y=6 solving systems of linear equations.solve by addition elimination 3x-6y=5 2      Log On


   

Question 188887: solving systems of linear equations.solve by substitution
2x+y=10
3x-4y=26
y=2x+3
3x+2y=6
solving systems of linear equations.solve by addition elimination
3x-6y=5
2x-4y=8

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Solving systems of linear equations.Solve by substitution
2x+y=10, EQN 1
3x-4y=26, EQN 2

In EQN 1 we get, y=10-2x--> EQN 3, substitute in EQN 2

3x-4%28highlight%2810-2x%29%29=26
3x-40%2B8x=26
11x=26%2B40=66 ---->cross%2811%29x%2Fcross%2811%29=cross%2866%296%2Fcross%2811%29
highlight%28x=6%29, substitute in EQN 3:

y=10-2%286%29=10-12=highlight%28-2%29

Intersect at point (6,-2)
--->RED, EQN1; GREEN, EQN 2

y=2x+3, EQN 1
3x+2y=6, EQN 2

Substitute EQN 1 in EQN 2:
3x%2B2highlight%28%282x%2B3%29%29=6
3x%2B4x%2B6=6
7x=6-6=0 ----> highlight%28x=0%29, subst. in EQN 1

y=2%280%29%2B3 ----> highlight%28y=3%29

Intersect at point (0,3)
---> RED, EQN 1; GREEN, EQN 2


Solving systems of linear equations. Solve by addition elimination
3x-6y=5, EQN 1
2x-4y=8, EQN 2

Multiply EQN 1 by -4, EQN 2 by 6, and then "add":
3x-6y=5x-4 ----> cross%28-12x%29%2Bcross%2824y%29=-20
2x-4y=8x6 -----> cross%2812x%29-cross%2824y%29=48

no solution. These lines don't intersect:

We'll look for the intercepts:
In EQN 1, let fy=0
3x-6%280%29=5 ---> cross%283%29x%2Fcross%283%29=5%2F3
red%28x=5%2F3%29
let fx=0
3%280%29-6y=5 ---> cross%28-6%29y%2Fcross%28-6%29=5%2F-6
red%28y=-5%2F6%29

In EQN 2, let Fy=0
2x-4%280%29=8 ---> cross%282%29x%2Fcross%282%29=cross%288%294%2Fcross%282%29
red%28x=4%29
Let fx=0
2%280%29-4y=8 ---> cross%28-4%29y%2Fcross%28-4%29=cross%288%292%2Fcross%28-4%29
red%28y=-2%29
---> RED, EQN 1; GREEN, EQN 2
Since they line on the same plane they are parallel


Thank you,
Jojo