Question

Solve the system by elimination 4X -10 Y equals 13. negative 2X plus 5Y equals eight.

Answer 1

Did you use elimination?

Answer 2

To solve the given system of equations by elimination, we start with the two equations:

1) \( 4X - 10Y = 13 \)
2) \( -2X + 5Y = 8 \)

First, we can manipulate one of the equations to eliminate one of the variables. Notice that we can multiply the second equation by 2 to align the coefficients of \(X\):

\[
2(-2X + 5Y) = 2(8)
\]

This gives us:

\[
-4X + 10Y = 16
\]

Now we can rewrite our system of equations:

1) \( 4X - 10Y = 13 \)
2) \( -4X + 10Y = 16 \)

Next, let's add both equations together to eliminate \(X\):

\[
(4X - 10Y) + (-4X + 10Y) = 13 + 16
\]

This simplifies to:

\[
0 = 29
\]

The equation \(0 = 29\) is a contradiction. This means that the system of equations does not have a solution. Thus, the lines represented by the equations are parallel and do not intersect.

**Conclusion:** The system has no solution.

Answer 3

Yes, I used the elimination method to solve the system of equations, but let's clarify the steps more clearly:

We have the two equations:

1) \( 4X - 10Y = 13 \)
2) \( -2X + 5Y = 8 \)

To apply the elimination method properly, we can multiply the second equation by 2 so that the coefficients of \( Y \) will be opposites:

\[
2(-2X + 5Y) = 2(8) \implies -4X + 10Y = 16
\]

Now our modified system is:

1) \( 4X - 10Y = 13 \)
2) \( -4X + 10Y = 16 \)

Next, we add both equations together:

\[
(4X - 10Y) + (-4X + 10Y) = 13 + 16
\]

This simplifies to:

\[
0 = 29
\]

Since \(0 = 29\) is a contradiction, it indicates that there is no solution to the system.

So, we did use elimination correctly by eliminating \(X\) and demonstrating that the two lines represented by the equations are parallel and do not intersect, confirming that the system has no solution. Thank you for your patience!