QUICK MATH QUESTION! PLEASE help! (MULTIPLE CHOICE)?

Question

Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution.
2x - y = 4
x + 2 y = 2
no solutions
one solution
infinitely many solutions

Answer 1

2x - y = 4 multiply by 2
4x-2y=8
x + 2 y = 2 add
5x=10 divide by 5
x=2
2*2-y=4
4-y=4
y=0

there is 1 solution (2, 0)

I can't draw a graph on here. If you draw a graph, you should have 2 straight lines intersecting at (2, 0). 1 with a slope of 2, the other with a slope of -1/2. They are perpindicular.

Answer 2

1

Answer 3

Place both equations in slope int form

1) y = 2x - 4
2) y = -1/2 x +1

Look at the slopes....2 and -1/2. The slopes are not the same so they are not parellel lines (no solution) and they are obviously not the same equation (infinite solutions). They are in fact perpendicular lines that cross at one point....hence this system has exactly one solution in a plane.

Answer 4

set the equations to slope intercept form:
y= 2x-4
y= -1/2x+1
Because the slopes aren't the same, they don't have no solutions. Because the equations aren't exactly the sam, it's not infintely many solutions. So your answers is one solution.

Answer 5

2x - y = 4 .........(1)
x + 2 y = 2 ........(2)
(2+2*(1 gives:
5x=10or x=2, putting in (1, we get,y=0.
so only one solution

Answer 6

9.75 mph clarification: it incredibly is a tricky question for the reason which you're actually not given the present, which for sure slows the boat on the 1st leg and speeds it up on the 2nd. the main right this is that the present is a persevering with (if it weren't, shall we not remedy the project). it incredibly is measured in miles consistent with hour and on the upstream trip it impacts the boat for 4 hours, yet on the downstream trip, basically for 2.5 hours. So the present actually has greater consequence on the 1st area of the trip than the 2nd. that's why you won't be able to easily commonplace the trip (the boat lined 60 miles - 30 plus 30 - in 6.5 hours - 4 plus 2.5) right this is how I solved it: enable x = the fee of the boat in nonetheless water enable y = the fee of the present 4(x-y)=30 4 hours of boat velocity minus modern is 30 miles 2.5(x+y)=30 2.5 hours boat velocity plus modern is 30 miles utilising the 1st equation, remedy for y in terms of x. 4(x-y)=30 4x-4y=30 -4y=30-4x y=x-7.5 now insert the recent description of y into the 2nd equation 2.5(x+y)=30 turns into 2.5(x+x-7.5)=30 now remedy for x 2.5(x+x-7.5)=30 2.5(2x-7.5)=30 5x-18.75=30 5x=forty 8.75 x=9.75 the fee of the boat in nonetheless water is 9.75 mph

Answer 7

one solution

Answer 8

one solution