How to solve systems of equations

to solve this equation it is hard to show especially with this kind of graph because it automatically gives you the answer but typically you would start at the y intercept (B) and then go along with the slope

Systems of equations

in systems of equations there are 3 ways to solve.

1.graphing

2.substitution

3.elimination

Graphing

1. re write equations in slope intercept form (y=mx+b)

2. graph the line

3. identify solutions

with systems of equations there are 3 possible main ways an equation can be solved

intersecting = one solution (the point where the lines meet)

parallel= no solution (the lines never touch)

same line = infinite solutions

EX intersecting

y=\frac23x-1

y=-1x+4

with these 2 equations you would graph them and then you would find the point where they would meet. in this case the point is (3,1) there for the answer is (3,1)

EX parallel

y=x+5

x-y=2

if you graph both of these it shows how the lines never meet

EX Same line

x+2y=4

y=-\frac12x+2

and as you can see when you graph it it has the same line

Subsitution

1. solve one equation for x or y

2. substitute this expression on the other equation and solve for the variable

3. substitute your answer into the revised equation from step one and solve for the other variable

EX intersecting

y=4x-1

y=2x-5

steps to sove

4x-1=2x-5

-2x\ldots-2x

2x-1=-5

..+1\ldots+1

\frac{2x}{2}=\frac{-4}{2}

x=-2

as you can see first solve one of the equations then solve ethire x or y in this example we would solve for y since we just solved for x

y=4\left(-2\right)-1

y=-8-1

y=-9

(x,y) (-2,-9)

EX parallel

x-2y=-2

x-2y=2

as you can see the base of the equations are the same but the answers are diffrent therefor making it no soulution because the lines never meet

elimination

1. make sure equations are lined up

2. add or subtract the equation to eliminate the variable with the coefficient

3. solve for the remaining variable

4. substitute your answer into either the original equation and solve for the other variable

   (this is very self explanatory and i am so done with doing this s**t)