SOLUTION: i) Solve the following system of equations graphically by first finding both intercepts for the straight line represented by each equation: x-3y=3 & 2x+y=2 Estimate values for yo

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: i) Solve the following system of equations graphically by first finding both intercepts for the straight line represented by each equation: x-3y=3 & 2x+y=2 Estimate values for yo      Log On


   

Question 556829: i) Solve the following system of equations graphically by first finding both intercepts for the straight line represented by each equation:
x-3y=3 & 2x+y=2
Estimate values for your solutions to one decimal place.
ii) Check your answer from the above question by solving the set of equations algebraically.
Help me, please.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
first equation is x - 3y = 3
add 3y to both sides of the equation and subtract 3 from both sides of the equation to get:
3y = x-3
divide both sides of the equation by 3 to get:
y = (x-3)/3
second equation is 2x + y = 2
subtract 2x from both sides of this equation to get:
y = -2x + 2
those are the equations you want to graph.
you will get:
graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%28x-3%29%2F3%2C-2x%2B2%29
the intersection of these 2 lines looks like it will be somewhere between x = 1 and 2, and between y = 0 and -1
if i had to guess based on what the graph is showing, i would guess that:
x = 1.2
y = .5
the actual intersection of those lines can be found by solving the equations simultaneously.
the first equation is:
x - 3y = 3
the second equation is:
2x + y = 2
multiply the first equation by -2 to get:
-2x + 6y = -6 (first equation multiplied by -2)
2x + y = 2 (second equation)
add the equations together to get:
7y = -4
divide both sides of this equation by 7 to get:
y = -4/7
the decimal equivalent of this is y = -.5714286
substitute -4/7 for y in one of the original equations to get:
x - 3y = 3 becomes:
x - 3(-4/7) = 3 which becomes:
x + 12/7 = 3
subtract 12/7 from both sides of this equation to get:
x = 3 - 12/7 which becomes:
x = 21/7 - 12/7 which becomes:
x = 9/7
the decimal equivalent of this is 1.2857143
the intersection of the 2 lines is at:
x = 1.2857143
y = -.5714286
the algebraic solution supports the graphical solution.
the answer, rounded to 1 decimal place is:
x = 1.3
y = -.6
the eyeball from the graph was fairly close to the actual intersection but not right on.
if i had enlarged the graph and did some measurements, i might have been able to get closer, but would never get to the accuracy i got by solving the equations simultaneously without a huge expenditure of time and energy.
if all you have is the graph then you would take your best measurement.
if you can solve by equation, then the equation will get you the most accurate answer.