Question 130322This question is from textbook
: can you assist me with the following problems
1. determin wether the system has one solution, no solution or infinitely solution. y=2/3x and 2x-y=-4
2.use elimination to solve x/2 + 2y =9 and 2x-y =18
3. use elimination to solved. 4x-y=-3 and sx+2y = -20
4.find the solution of the system y=x2+5 and y = 2x+4
This question is from textbook
Answer by cngriffith(27)   (Show Source):
You can put this solution on YOUR website! problem 1.
y=2/3x+0 slope =2/3 b=o
y=mx+b slope intercept formula: m=slope b=y intercept
2x-y=-4 solve for y, this puts the equation in y=mx+b form
-y=-2x-4 subtracted 2x from both sides
y=2x+4 divided both sides by -1 m=2 b=4
Therefore one solution because:
Different slopes means the graphs will intersect in one point. If the m's are = and the b's different then no solution because the graphs will never intersectbecause the lines are parallel. You have infinitely many solutions when the m's are the same and the b's are the same because one line will graph on top of the other line. This means the two lines intersect at all points.
problem 2 The first equation
x/2+2y=9 solve for x begin by subtracting 2y from both sides
x/2=-2y+9 multiply both sides by 2 to get rid of the denominator
x=-4y+18
The second equation
2x-y=18 solve for x, add y to both sides
2x=y+18 now divide both sides by 2
x=(y+18)/2
Equate your two answers resulting from both equations solved for x
-4y+18=(y+18)/2 you could make it a proportion by placing a 1 under the
left side
(-4y+18)/1=(y+18)/2 now cross multiply
-8y+36=y+18 solve this equation
-9y=-18
y=2
Take either one of the original equations and substitute 2 for y and solve for x.
2x-y=18
2x-2=18
x=10
problem 3. Have you typed this problem in correctly?
Problem 4. Using y=mx+b the slope of the first equation is 2 and the slope of the second equation is also 2. This means the lines are parallel and there is no point of intersection, hence no solution.
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