Question

Use algebraic rules of equations to predict the solution type to the system of equations. Include all of your work for full credit.

Answer 1

one solution

Explanation:

First one:

`x+y=-4\\y=-x-4`

Second one:

`y=2x-1`

Here,

the slope of the first one is not the same as the second one. So, this tells us that they are neither parallell nor the same equation. Therefore this system of equation will have one unique solution

Answer 2

(5;-9)

Explanation:

If we use the rules, we can predict a possible result, because we observe that y-variable can be eliminated without any operations. So:

`\left \{ {{x+y=-4} \atop {y=2x-1}} \right. \\x+0=2x-5\\5=x`

So, we already have the first solution. Replacing this value to find the second one:

`x+y=-4\\5+y=-4\\y=-4-5=-9`

Therefore, the solution is (5;-9)