SOLUTION: Solving a System of Equations. Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in ordered-pair form. 3/4x+1/2y=5 -1

Question 1128374: Solving a System of Equations. Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in ordered-pair form.
3/4x+1/2y=5
-1/4x-3/2y=1
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Solve the System of Equations by Graphing

Let's look at the first equation

Multiply both sides of the first equation by the LCD 4

Distribute

---------

Let's look at the second equation

Multiply both sides of the second equation by the LCD 4

Distribute

---------

So our new system of equations is:

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (green)

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

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Your system can be read in this way ((3/4)x + (1/2)y = 5, (-1/4)x - (3/2)y = 1, or in this way 3/(4x) + 1/(2y) = 5, -1/(4x) - 3/(2y) = 1, depending on how to put PARENTHESES into equations. So, the way you presented the problem is AMBIGOUS. To avoid ambiguity, YOU must put parentheses in your formula BEFORE POSTING IT TO THE FORUM.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Solving a System of Equations. Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in ordered-pair form.
3/4x+1/2y=5
-1/4x-3/2y=1

That's the most inefficient, most time-consuming, and most error-prone method I've ever seen one use to solve a system of equations,
if I ever saw one. It is so inefficient and CONFUSING to the point where the woman who solved it got WRONG solutions. Her solutions
DO NOT SATISFY THE EQUATIONS, so IGNORE HER ENTIRE SOLUTION. Plus, why would someone even try to solve a fractional system by graphing? RIDICULOUS!
I assume the system is: ------ eq (i)
---- eq (ii)
Just multiply eq (ii) by 3 to get: ---- eq (iii)
Adding eqs (i) & (iii) results in:

- 4y = 8

Substitute - 2 for y in any of the original equations and you should get:
That's all! Nothing more, nothing less!!
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