Question 112097


{{{y=2*x-1}}} Start with the given equation



Let's test the first solution (0,-2):



{{{(-2)=2*(0)-1}}} Plug in {{{x=0}}} and  {{{y=-2}}}



{{{-2=-1}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (0,-2) is <font size=4><b>not</b></font> a solution to {{{y=2*x-1}}}




-------Now lets test another solution-------




Let's test the second solution (0,-1):



{{{(-1)=2*(0)-1}}} Plug in {{{x=0}}} and  {{{y=-1}}}



{{{-1=-1}}} Simplify. Since the two sides of the equation are equal, this means (0,-1) is a solution to {{{y=2*x-1}}}




-------Now lets test another solution-------




Let's test the third solution (1/2,0):



{{{(0)=2*(1/2)-1}}} Plug in {{{x=1/2}}} and  {{{y=0}}}



{{{0=0}}} Simplify. Since the two sides of the equation are equal, this means (1/2,0) is a solution to {{{y=2*x-1}}}




-------Now lets test another solution-------




Let's test the fourth solution (3,-5):



{{{(-5)=2*(3)-1}}} Plug in {{{x=3}}} and  {{{y=-5}}}



{{{-5=5}}} Simplify. Since the two sides of the equation are <font size=4><b>not</b></font> equal, this means (3,-5) is <font size=4><b>not</b></font> a solution to {{{y=2*x-1}}}



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Answer:

So the following ordered pairs are solutions to {{{y=2*x-1}}}


(0,-1) and  (1/2,0) 


Now let's graph the equation {{{y=2*x-1}}} and plot the points (0,-2), (0,-1), (1/2,0), and (3,-5)

{{{drawing(900,900,-10,10,-10,10,
graph(900,900,-10,10,-10,10,2*x-1),

circle(0,-2,0.08),
circle(0,-2,0.10),
circle(0,-1,0.08),
circle(0,-1,0.10),
circle(1/2,0,0.08),
circle(1/2,0,0.10),
circle(3,-5,0.08),
circle(3,-5,0.10),
green(circle(0,-1,0.05)),
green(circle(0,-1,0.08)),
green(circle(1/2,0,0.05)),
green(circle(1/2,0,0.08)))}}}

Here we can see that the points (0,-1) and  (1/2,0)  lie on the line (they are the green points). These are the solutions to the equation {{{y=2*x-1}}}. 

Notice the other possible solutions are points that do not lie on the line. Those ordered pairs do not satisfy the equation {{{y=2*x-1}}}