One solution equations*

So One Solution equation with two variable from system of equation is quite similar to One Solution equation from one variable equation because both have One solution. To solve the equation for system of equation, we’re going to eliminate the two equation to get the value x and y. We use system of equation to find the slope and intercept points for our graph, that’s how the two is connected. However, we’re also going to demonstrate this equation using word problem to show how you can change the sentence to algebraic form.

 

Example: 1. system of equation with one solution. 

y=5x+3

y=7x+3

x=? y=?

Solution:                                       Let’s take a look at the system…

Let’s first find the solution to y

y=5x+3

y=7x+3

Add coefficient 7 to the first equation and 5 to the second equation. The reason we add them because our goal is to eliminate one variable to find another variable

7(y=5x+3)

5(y=7x+3)

Multiply or distribute the equation from the parentheses

7*(y=5x+3)

5*(y=7x+3)

=>

7y=35x+21

5y=35x+15

Now we can eliminate y along with

     7y  =   35x+21

 –   5y =  35x+15

2y=0x+6

Since x has no value after multiplying , we are left with

2y=6

 =>y= 6/2 = 3

So we get y = 3

Now find x, we just substitute the y value with the equation:

y=5x+3

3=5x+3

Solve the equation…

5x=3-3

x= 0/5

=>x = 0/5= 0

y =3 and x =0

There for, this system of equation is a consistent with independent equation.

Word Problem: The combined average weight of an iPhone X and a Samsung galaxy s8 is 5 kilograms. The average weight of 3 iPhone X is 7 kilograms more than the average weight of one elephant.

On average, how much does an iPhone X weighs, and how much does a Samsung galaxy s8 weigh?

Let x represent the average weight of an iPhone X and let y represent the average weight of a Samsung galaxy s8.  Since we have two unknowns, we need two equations to find them.

Let’s use the given information in order to write two equations containing x and y For instance, we are given that the combined average weight of an iPhone X and a Samsung galaxy s8 is 5 kilograms. How can we model this sentence algebraically?

Since their combined average weight is 5 kilograms, we get the following equation:

x+y=5

We are also given that the average weight of $\text{3}$ iPhone X is 7 kilograms more than the average weight of one Samsung galaxy s8. This can be expressed as:

x+7=3y

Let’s rewrite this equation so that it’s solved for x:

x=3y−7

Now that we have a system of two equations, we can go ahead and solve it!

Let’s substitute x=3y−190 into the first equation:

x+y=5

(3y−7)+y=5         

       4y=5+7

     4y=12

          y = 12/4

    y =3

Now we can substitute y=3 into x+y=5 and find that x=2