Question

Solve the system of equations

-4x+6y=38
x-5y=-20 (1 point)

Answer 1

How many solutions does the system of equations have?

-5x+y=-18
10x-2y=36 (1 point)

Answer 2

To solve the system of equations, we can use the method of substitution.

From equation (2), we can express x in terms of y:

x = 5y - 20

Substitute this value of x into equation (1):

-4(5y - 20) + 6y = 38

Simplify the equation by distributing:

-20y + 80 + 6y = 38

Combine like terms:

-14y + 80 = 38

Subtract 80 from both sides:

-14y = -42

Divide both sides by -14:

y = 3

Now substitute this value of y into equation (2) to find x:

x - 5(3) = -20

x - 15 = -20

Add 15 to both sides:

x = -5

Therefore, the solution to the system of equations is x = -5 and y = 3.

Answer 3

To determine the number of solutions that the system of equations has, we can use the method of elimination.

First, let's multiply the first equation by 2:

-5(2x) + 2y = -18
-10x + 2y = -18

Now, we can write the system of equations together:

-10x + 2y = -18
10x - 2y = 36

When we add the two equations together, the y terms cancel out:

-10x + 2y + 10x - 2y = -18 + 36
0 = 18

We are left with 0 = 18, which is not a true statement. This tells us that there are no solutions to the system of equations.

Therefore, the system of equations has no solutions.