Please help with these 2 algebra questions?

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The three Math Idol judges have been eliminating contestants all day! The number of one-step equations and two-step equations who have been eliminated today is equal to 1070! If three times the number of one-step equations minus twice the number of two-step equations is equal to 110, how many one-step equations auditioned today?
900
620
520
450
What is the value of the x variable in the solution to the following system of equations?
4x + 8y = 8
x + 2y = 2
0
2
There is no x value as there is no solution to this system
x can be any value as there are infinitely many solutions to this system

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Answer by
I think there might be something wrong with the phrasing of the first question. The second sentence, with the number of equations eliminated equaling 1070, can be turned into x + y = 1070 (with x being the number of one-step equations and y being the number of two-step equations). But the next sentence doesn't say if the equations it's talking about are the ones eliminated, or the number that auditioned. It doesn't really make sense. If the two sentences were talking about the same thing, you could have these two equations:
x + y = 1070
3x - 2y = 110
From the first equation, x = 1070 - y
Plug that into the second equation
3(1070 - y) - 2y = 110
3210 - 3y - 2y = 110
3210 - 5y = 110
3210 - 110 = 5y
5y = 3100
y = 620
Plug that into the first equation
x + 620 = 1070
x = 1070 - 620
x = 450
450 one-step equations and 620 two-step equations
______________
4x + 8y = 8
x + 2y = 2
From the second equation, x = 2 - 2y
Plug that into the first equation
4(2 - 2y) + 8y = 8
8 - 8y + 8y = 8
8 = 8
Since 8 always equals 8, x can be any value as there infinitely many solutions to this solution. You can check it:
4(16) + 8y = 8
64 + 8y = 8
8y = -56
y = -7
16 + 2(-7) = 2
16 - 14 = 2
2 = 2

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Answer by
I don't know the first one, sorry. But I know the second one
you want to cancel out a variable, so you can either substitute: x=-2y+2, so substitute -2y+2 in x in the other equation: 4(-2y+2)+8y=8 and solve for y (which will allow you to solve for x quite easily by plugging that # in for y in one of the equations)
or you can cancel out one of the variables by multiplying (this is my favorite way). Say you want to cancel out the y's. you can multiply the second equation by -4, which will get you -4x - 8y=-8
and then subtract this from the previous equation:
4x + 8y =8
-4x - 8y= -8
_________
0x 0y = 0
therefore, 0=0. This means that x can be any value (infinite solutions) whenever both variables are zero and the answer is zero (8-8=0), then there are infinite results.
If however, the answer is like 0x+0y=4, there is NO SOLUTION, because 0 cannot equal 4.
Hope this helps. Sorry it's really long haha
Answer by
Call the questions T and O:
[The number of one-step equations and two-step equations who have been eliminated today is equal to 1070]
T + O = 1070
[! If three times the number of one-step equations minus twice the number of two-step equations is equal to 110]
3O - 2T = 110
Use equation 1 to express T in terms of O by subtracting O from both sides:
T + O = 1070 becomes T = 1070 - O
Substitute 1070 - O for T:
3O - 2T = 110 becomes 3O - 2(1070 - O) = 110
Multiply out:
3O - 2140 + 2O = 110
Simplify:
5O - 2140 = 110
Add 2140 to both sides:
5O = 2250
Divide both sides by 5:
O = 2250 / 5 = 450
There were 450 one-step questions.
What is the value of the x variable in the solution to the following system of equations?
4x + 8y = 8
x + 2y = 2
Dividing through equation 1 by 2 gives you equation 2:
What is the value of the x variable in the solution to the following system of equations?
(4x + 8y = 8) / 4 ==> x + 2y = 2
Since the equations are the same, the lines overlap and there are an infinite number of solutions. (answer 4)