Solve the system of two linear equations

To solve this system of equations, we will use the method of substitution or elimination.

Given equations:
1. -3x - 4y = -23
2. 3x - 5y = 5

First, we simplify equation 1 by multiplying by -1 to make the y coefficients match:
3x + 4y = 23

Next, we will add equation 1 and equation 2 to eliminate the x variable:
-3x - 4y + 3x - 5y = -23 + 5
-9y = -18
y = 2

Now, we substitute the value of y back into either equation 1 or equation 2 to solve for x:
3x - 5(2) = 5
3x - 10 = 5
3x = 15
x = 5

Therefore, the solution to the system of equations is x = 5 and y = 2.

How many solutions does the system of equations have?

8 x − 6 y = 48
8 x + 6 y = 48

To determine the number of solutions for the system of equations, we can compare the coefficients of x and y in the two equations provided.

Given equations:
1. 8x - 6y = 48
2. 8x + 6y = 48

If we compare the coefficients of x and y in the two equations, we can see that the coefficients for both x and y are the same, just with different signs. This means that the lines represented by the equations are parallel.

Since the lines are parallel, they will never intersect and hence there are no solutions to the system of equations.

Therefore, the system of equations has no solutions.

are you sure recheck

Apologies for my error in the previous response. Let's reanalyze the system of equations provided:

Given equations:
1. 8x - 6y = 48
2. 8x + 6y = 48

If we compare the coefficients of x and y in the two equations, we see that the coefficients for x are the same but the coefficients for y are opposite in sign. This suggests that the lines represented by these equations are parallel.

However, when we look closely, we see that the constant terms on the right-hand side of both equations are also the same. This means that the two equations represent the same line.

Therefore, the system of equations has infinitely many solutions, since the equations are equivalent and represent the same line. Apologies for the confusion in the previous response. Thank you for bringing it to my attention.

im not sure thats a sufficeint answer

I apologize for the confusion. Let's further analyze the system of equations to determine the number of solutions:

Given equations:
1. 8x - 6y = 48
2. 8x + 6y = 48

If we add the two equations, we get:
(8x - 6y) + (8x + 6y) = 48 + 48
16x = 96
x = 6

Now that we have found the value of x, we can substitute it back into one of the equations to solve for y. Let's use the first equation:
8(6) - 6y = 48
48 - 6y = 48
-6y = 0
y = 0

The solution to the system of equations is x = 6 and y = 0. Therefore, the system of equations has a unique solution. Thank you for your patience, and I apologize for the oversight in the previous responses.