SOLUTION: Determine which of the following points are solutions to the system of equations. {3x + 2y =5 {x + 2y = 7 A. (3, 0) B. (−1, 4) C. (3, 0) D. (4, −1) Pleas

Algebra ->  Expressions -> SOLUTION: Determine which of the following points are solutions to the system of equations. {3x + 2y =5 {x + 2y = 7 A. (3, 0) B. (−1, 4) C. (3, 0) D. (4, −1) Pleas      Log On


   

Question 827923: Determine which of the following points are solutions to the system of equations.
{3x + 2y =5
{x + 2y = 7
A. (3, 0)
B. (−1, 4)
C. (3, 0)
D. (4, −1)
Please show work
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:


3x%2B2y=5

1x%2B2y=7





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


3x%2B2y=5 Start with the given equation



2y=5-3x Subtract 3+x from both sides



2y=-3x%2B5 Rearrange the equation



y=%28-3x%2B5%29%2F%282%29 Divide both sides by 2



y=%28-3%2F2%29x%2B%285%29%2F%282%29 Break up the fraction



y=%28-3%2F2%29x%2B5%2F2 Reduce



Now lets graph y=%28-3%2F2%29x%2B5%2F2 (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+%28-3%2F2%29x%2B5%2F2%29+ Graph of y=%28-3%2F2%29x%2B5%2F2




So let's solve for y on the second equation


1x%2B2y=7 Start with the given equation



2y=7-x Subtract +x from both sides



2y=-x%2B7 Rearrange the equation



y=%28-x%2B7%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%287%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B7%2F2 Reduce





Now lets add the graph of y=%28-1%2F2%29x%2B7%2F2 to our first plot to get:


Graph of y=%28-3%2F2%29x%2B5%2F2(red) and y=%28-1%2F2%29x%2B7%2F2(green)


From the graph, we can see that the two lines intersect at the point (-1,4) (note: you might have to adjust the window to see the intersection)



answer: B. (−1, 4)