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Question 751679: i am supposed to use substitution to solve this she said the answer is infinate but could you explain how?
-2x-5y=-25
y= -2\5x+5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you convert both these equation to standard slope intercept form, you will see that the equations are identical (exactly the same).
this means they represent the same line.
this means all solutions valid for one line are also valid for the other line.
this means you have an infinite number of solutions (any point on the line will satisfy both equations).
to solve using substitution, you would do the following:
first equation is -2x - 5y = -25
second equation is y = - (2/5)x + 5
replace y in the first equation with -(2/5)x + 5 from the second equation.
you will get:
-2x - 5(-2/5)x + 5) = -25
simplify this to get:
-2x + 2x - 25 = -25
combine like terms to get:
-25 = -25
the variable dropped out of the equation and the equation is true (-25 really does equal to -25).
this means you have infinite number of solutions and any value of x or y that you pick will satisfy both equations.
for example, take x = 5
-2x -5y = -25 becomes -2(5) - 5y = -25 which becomes -10 - 5y = -25 which becomes -5y = -15 which becomes y = 3.
when x = 5 in one equation, y = 3.
substitute these values for x and y in the second equation to get:
y = (-2/5)x + 5 becomes 3 = (-2/5)(5) + 5 which becomes 3 = -2 + 5 which becomes 3 = 3.
you can pick an infinite number of values of x and solve for y in one equation and that pair of values will be solutions of the other equation.
this stand to reason since both equations will graph the same line.
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