Hi, I was wondering if someone could explain to me step by step how to do this type of problem.?

Question

It says Find 3 solutions of the equation 4x+3y=14. Thank you very much.

Answer 1

first, one of the things you could do is plug in 0 for x

4(0) + 3y = 14
0 + 3y = 14
3y = 14
y = 3/14
so, one of the solutions is x=0 and y=3/14
also, it can be written as (0, 3/14)

you can also plug in 0 for y

4x + 3(0) = 14
4x + 0 = 14
4x = 14
x = 4/14
so your second solution is x = 4/14 and y = 0
also, it can be written as (4/14, 0)

fpr your third solution, you can plug in any number you want for either x or y. it doesn't matter which number you plug in and to which variable (x or y).

let's try plugging in 1 for x for example

4(1) + 3y = 14
4 + 3y = 14
3y = 11
y = 11/3
so your third solution is x = 1 and y = 11/3
also, it can be written as (1, 11/13)

for future problems, you can just plug in any number for either variable (x or y) and solve for the other variable.

i hope that helped

Answer 2

well you can pretty much plug any number in for x and then find y.
For Example:
4(2) + 3y = 14
8 + 3y = 14
3y = 6
y = 2
so x = 2, y =2 is one solution (2, 2)

4 (5) + 3y = 14
20 + 3y = 14
3y = -6
y = -2
so x = 5, y = -2 is another solution (5, -2)

4 (8) + 3y = 14
32 + 3y = 14
3y = -18
y = -6
So x = 8, y = -6 is another solution (8, -6)

there are many other solutions for this problem. You can pretty much put ANY number in. If you know how to graph that line you should be finding points that fall on that line

Answer 3

Well the equation you have is the equation of a line. This means that any point on the line satisfies the equation. There are therefore an infinite number of solutions because there are an infinite number of points on the line.

Take some easy ones:

set x=0 then solve: you get y= 14/3, so (0,14/3) is a solution.

set y=0 then solve: you get x = 14/4, so (14/4,0) is a solution.

you can find other solutions by setting x or y to a value and then solving for the other coordinate.

Answer 4

You have a problem with two unknowns. You need to:

1. Solve for one unknown first.
2. Do this by subtracting or adding to isolate one of your variables on one side of the equation. You use the opposite action to what you have (if you have a + number, subtract; if you have a - number, you add).
3. Now you want to have this isolated variable by itself. For example if you subtract -y from both sides of the equation to isolate 4x, then you need to isolate the x variable by dividing both sides by 4.

5. Now you have the x variable in terms of the y variable.

6. Go back to your original problem and insert your answer for x in the place where your x variable is.

7. Now, solve for the y variable.

When you get this done, go back to your problem and start by isolating the OTHER variable (for example, if you isolated x the first time, isolate the y this time). Follow the same kind of steps to find out the value of the y variable in terms of the x variable.

Now, go back and insert your answer for the y variable into the original problem where the y is and then solve for x.

The these two steps will give you values for both x and y (two ways to solve the problem).

The 3rd and 4th way to solve the problem is to start with the original equation and solve for one of the variables. Your answer will be in terms of the other variable. Do this for both of your variables and you have two solutions (you just won't solve for a numerical value of the variables.)

Let's do it:

4x + 3y = 14
First, isolate x by subtracting 3y from both sides.

This gives you:
4x = 14 - 3y

Now, divide both sides by 4 to isolate and solve for x:

x = 14 - 3y/4 (This is one solution for x)

Do the same thing again, but this time subtract 4x from both sides to isolate y:

3y = 14 - 4x
Now to isolate and solve for y, divide both sides by 3:

y = 14 - 4x/3 (this is a second solution)

The above to solutions do not give you a specific value for x and y (these are examples of the last part of my instructions.)

To get specific values for your variables you need to replace x or y with one of your solutions in your original equation:

4x - 3y = 14
(Our solution for x in terms of y was x = 14 -3y/4. Substitute this value for x in the equation and then solve for y)

4(14-3y/4) - 3y = 14
This will give you the value for y and your 3rd solution.

Do the same thing for y. Use the value you got for y in terms of x and substitute this for the y variable and solve for x. This is your fourth solution to the problem.

I think you can do the math from here.

Hope this helps.

Answer 5

first u solve for y, it would be y=-4/3x+14, and then u plug in anything for x, and the answer is y, so if u do that 3 times u get (x,y), and u that is a solution

Answer 6

There is no solution possible without another equation.
4x+3y=14
x= (14-3y)/4
y=(14-4x)/3
This is the furthest you can go.

Answer 7

(2,2), (5,-2), (-1,6)