Question

The system of equations is inconsistent.
What are the missing values?
5x+___y=2
___x+3y=8

Answer 1

inconsistent means there will not be a solution to the system of two lines. In other words, the two lines will not intersect, and are parallel.

Answer 2

how would i find the answers to the blank spaces then?

Answer 3

An easy way to determine if two lines are parallel from the given form above...

Ax + By = E
Cx + Dy = F

If the constants are a multiple of one another than the lines are parallel. If you can multiply, Ax+By by some number , and get Cx+Dy, the lines will be parallel.

Answer 4

So if you let the first equation be...

5x + 1y = 2

you can see that the second equation will be 3 times the first, The first will have 1y, and the second has 3y.
So you have to multiply the 5x by 3

Answer 5

3*(5x + 1y) ---> 15x + 3y

Here is a good reference for these types of probs...
http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson

Answer 6

thanks for explaining that :)

Answer 7

A step further, if you multiply the first equation by a constant number, and not only the values on the X and Y become the same, but also the value on the Right of the = sign becomes the same, then Both are the same line.
For example

4X + 5Y = 5
8X + 10Y =10

The second equation is just 2 times the first equation. Both are the same line, they overlap. They have Infinitely many solutions, and are dependent.

Answer 8

yeah, it was actually 3 and 5

Answer 9

that is possible too. As long as the coefficients on X and Y in the second line are a multiple of the coefficients of X and Y in the second line.

Using 3 and 5, means that they used a multiple of 1.