Use the substitution method to solve this system:?

Question

x - 4y = -10
2x - 8y = -17

A: Dependent (many solution)

B: (2 , 3)

C: (2 , 4)

D: Inconsistent (no solution)

Answer 1

x - 4y = -10, so x = 4y - 10.
Now substitute this equality for x in the other equation.
2x - 8y = -17
2(4y - 10) - 8y = -17
8y - 20 - 8y = -17
-20 = -17
This is inconsistent! There are no values for x and y which make both equations true. The answer is D.

Answer 2

Okay. First, rewrite the first equation:

x - 4y = -10
(+4y)
=> x = 4y - 10
=> 2x - 8y = -17 (original second equation)

Now we have x = to a value, so we can substitute that value in for x in any other equation in the system. Lets substitute it in for x in the second equation:

2(4y - 10) - 8y = -17
And now we need to solve for y within this equation. First lets distribute the 2.

8y - 20 - 8y = -17
=0y - 20 = -17
(+20)
0 = 3
Since the end result of substitution with this system of equations is not equal, this means that there is no solution to the system. When you see this, you can conclude that the two equations in the system express parallel lines, because parallel lines are the only lines that have no solutions that work on both line. If you were to get an equal result, that would mean that there was an infinite amount of solutions, which would mean that the lines expressed by the equations are actually the same line.

So, the solution to this equation is non-existent, and the answer is D.

Answer 3

Rearrange the problem
x-4y=-10 Add 4y to both sides
x=4y-10


Substitute (4y-10) for x in the second equation
2(4y-10)-8y=-17 Distribute the 2
8y-20-8y=-17 Add 20 to both sides
8y-8y=3
0=3 impossible

Answer
D: inconsistent (no solution)

Answer 4

D: Inconsistent (no solution)

Answer 5

if you multiply the top by -2
-2x+8y=20
2x-8y=-17
0=3
so the answer is d.