Question 1018020: Solve the system using the elimination method. Check your answer. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.)
g = −0.1f + 6.9
f + 10g = 69
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe this will give you an infinited number of solutions.
your two equations are g = -.1f + 6.9 and f + 10g = 69
take the first equation and put it in a similar form to the second equation as follows:
start with g = -.1f + 6.9
add .1f to both sides of the equation to get .1f + g = 6.9
multiply both sides of this equation by 10 to get f + 10g = 69
your two equations are identical.
the first equation is f + 10g = 69
your second equation is f + 10g = 69
this means you have an infinite number of solutions.
you could also have put both equations in y = mx + b form.
this form is the slope intercept form of the equation of a straight line.
m is the slope and b is the y-intercept.
if the slope is the same and the y-intercept is different, then the lines are parallel and there is no common solution.
if the slope is the same and the y-intercept is the same, then the lines are identical and there is an infinite number of solutions.
you can leave g = -.1f + 6.9 as is, since it is already in y = mx + b form.
start with f + 10g = 69
subtract f from both sides of this equation to get 10g = -f + 69
divide both sides of this equation by 10 to get g = -.1f + 6.9
the equations are identical because their slopes are the same and their y-intercepts are the same.
this means there is an infinite number of solutions that will solve both equations simultaneously.
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