Here are some things you should know when solving algebraic equations.
If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.
You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.
To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.
The distributive property is another important rule you will need to understand.
The distributive property is used mostly for simplifying parentheses in expressions/equations.
For example, how would you get rid of the parentheses here?
6(x + 1)
If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves.
The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6
Consider the first equation : -3x-8=19.
Adding 8 to both sides, we get -3x=27. Dividing by -3 yields the solution x=-9.
Consider the first equation : -3x-2=25.
Adding 2 to both sides, we get -3x=27. Dividing by -3 yields the solution x=-9, again.
Thus, the 2 equations have the same solution.
We could have achieved this result also by noticing that the second equation is equivalent to first one, adding 6 to both sides.
Answer: A) The equations have the same solution because the second can be obtained by adding 6 to both sides of the first equation.
Answer:
x = -4
Step-by-step explanation:
x+y = -10 -------- (1)
x-y = 2 ------- (2)
from (1)
x+y = -10
y = -10-x -------- (3)
substitute (3) into (2)
x-y = 2
x-(-10-x) = 2
x+10+x = 2
2x = 2-10
2x = -8
x = -8/2
x = -4
Answer:
5 (for c only)
Step-by-step explanation:
for c:
1st cleaning company: 
2nd cleaning company: 
set up as a system of equations. for them to cancle out make the y of one equation negative. I'll be making the second one negative ( it doesn't matter though)
it will look like:
make the two equations on top of eachother and line the terms up. Then combine them. The variable "y" will cancle out and you'll be left with
then you will add 3x to both sides to get 
then divide both sides by 3 to get 
if you plug in 5 for x into both of the original equations you will see that they will both make $100 in five hours. So you answer is 5
