Final answer:
The system of equations suggests there is a mistake as elimination results in a contradiction, indicating that the lines they represent are parallel and do not intersect.
Step-by-step explanation:
Solving the System of Equations Using Elimination Method
First, let's list the original equations given:
5x + 5y = 24
x + y = 4
This pair of equations are both linear and represent lines in a two-dimensional space. The goal is to find a point (x, y) where these two lines intersect. To do this, we will use the
elimination method
.
To apply the elimination method, we make the coefficients of one of the variables the same in both equations and then subtract or add the equations to eliminate that variable.
In this case, the second equation already has coefficients that are 1 for both x and y, so we can multiply the entire second equation by 5 to match the coefficients of the first equation:
(5x + 5y = 24) remains the same
(x + y = 4) multiplies by 5, becoming (5x + 5y = 20)
Now substract the second equation from the first:
(5x + 5y) - (5x + 5y) = 24 - 20
This simplifies to 0 = 4, which is a contradiction.
The resulting contradiction suggests that there is an error since the two equations given are not consistent and do not have a common solution, meaning that the lines they represent are parallel. There must have been a typo or mistake in the given equations. Normally, if the equations were correct and consistent, we would expect to find a single solution (x, y) after eliminating one of the variables.
Therefore, considering the contradiction, either there is a mistake in the equations given, or they represent a situation with no solution: the two lines never intersect.