Use substitution to determine which system is represented by the graph.

Answer:

2x + 4y = 28

-2y = x + 28

Step-by-step explanation:

Looking at the graph, we can see that the lines do not intersect. Therefore, they do not have a shared solution. We need to find the system of equations that does not have a solution.

1) Let's try to solve the third system given (counting from the top). To solve with the substitution method, we need to isolate one variable in one of the equations. I chose to isolate y in -2y = x + 28:

[tex]-2y = x + 28\\y = \frac{-1}{2}x -14[/tex]

2) Now that we've isolated the y in that equation, substitute what y equals in that equation for the y in the other equation. So, substitute [tex]\frac{-1}{2}x-14[/tex] for y in 2x + 4y = 28 and simplify:

[tex]2x + 4(\frac{-1}{2}x - 14) = 28\\2x - 2x- 64 = 28\\-64 = 28[/tex]

In a normal situation, the x's would not cancel out, and we would be able to isolate x to get the x-value of the solution. However, in this case, they have, and we ended up with a false statement, as -64 does not equal 28. Whenever this happens, it means the system does not have a solution. Therefore, the third option would represent the system in the graph.

The given graph shows the simultaneous relationship of equations 2x + 4y = 28 and  -2y = x + 28. Option C is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
From the graph, the two lines represents the simultaneous relationship,
Where,

The slope of the both lines is,
m = -1/2

And y-intercept of both lines is,
C₁ = 7 and C₂ = - 14

Now,
equations  of the lines are,
y = -x/2 + 7 and y = -x/2 - 14
x + 2y = 14  and x + 2y = -28
or
2x + 4y = 28  - - - - -  -(1) and  -2y = x + 28 - - - - - - -(2)

Now,
From equation 2 substitute y in equation 1
2x + 4[-x - 28]/2= 28
2x - 2x - 56 = 28
-56 = 28
So the lines are parallel and has no solution.

Thus, the given graph shows the simultaneous relationship of equations 2x + 4y = 28 and  -2y = x + 28. Option C is correct.

Learn more about simultaneous equations here:

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