6-1 Solving systems all 3 methods

Page 1

Substitution

y=3x+2 plug in for y

7x-4y=7

7x-4(3x+2)=7 distribute the 4

7x-12x-8=7 simplify

-5x-8=7

-5x=15

x=-3 plug in -3 to 1st equation

y=3(-3)+2

y=-9+2

y=-7

(-3,-7)

Elimination

3x+4y=10

2x-4y=14 cancel out the variable with one positive and one negative and add down for the other

5x=24 plug in answer and find the other value

{3x+4y=10

(2){2x-2y=5 multiply by whatever you have to to get the positive and negative term alike but do it to

3x+4y=10

4x-4y=10

y=3/2x+1 1 is the y intercept, graph it

rise over run with 3/2 start at the y point go up 3 and over 2

y=-x+6 6 is the y intercept, graph it

-1x is the slope put it over 1 if it's not a fraction

where both lines intersect the ordered pair is the answer

independent- intersecting lines with one solution

dependent- coinciding lines infinite solutions

inconsistent- parallel lines no solution

without graphing

if they have same slopes different y-intercepts= parallel lines

Substitution

Elimination

Graphing

classifying