SOLUTION: Solve the system by the best method. 4x + 6y = 4 4x + 6y = 10

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Question 446627: Solve the system by the best method.
4x + 6y = 4
4x + 6y = 10
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


4x%2B6y=4

4x%2B6y=10





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


4x%2B6y=4 Start with the given equation



6y=4-4x Subtract 4+x from both sides



6y=-4x%2B4 Rearrange the equation



y=%28-4x%2B4%29%2F%286%29 Divide both sides by 6



y=%28-4%2F6%29x%2B%284%29%2F%286%29 Break up the fraction



y=%28-2%2F3%29x%2B2%2F3 Reduce



Now lets graph y=%28-2%2F3%29x%2B2%2F3 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-2%2F3%29x%2B2%2F3%29+ Graph of y=%28-2%2F3%29x%2B2%2F3




So let's solve for y on the second equation


4x%2B6y=10 Start with the given equation



6y=10-4x Subtract 4+x from both sides



6y=-4x%2B10 Rearrange the equation



y=%28-4x%2B10%29%2F%286%29 Divide both sides by 6



y=%28-4%2F6%29x%2B%2810%29%2F%286%29 Break up the fraction



y=%28-2%2F3%29x%2B5%2F3 Reduce





Now lets add the graph of y=%28-2%2F3%29x%2B5%2F3 to our first plot to get:


Graph of y=%28-2%2F3%29x%2B2%2F3(red) and y=%28-2%2F3%29x%2B5%2F3(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.