Question

What is the solution to the system of equations below? 4x - y = 8; 5x + y = 1.

A) (1, -4)
B) (2, -3)
C) (3, -4)
D) (4, -5)

Answer 1

The solution to the system of equations is found by adding the two equations together to eliminate y and solve for x, and then substituting the value of x back into one of the original equations to find y. The solution is (1, -4), which is option A.

Step-by-step explanation:

To find the solution to the system of equations (4x - y = 8; 5x + y = 1), we can use the method of elimination or substitution. In this case, elimination appears to be the easiest method as the y variables can cancel each other out when we add the two equations together.

So, let's add the two equations:

• 4x - y = 8
• 5x + y = 1

By adding the two equations together, we obtain:

4x + 5x - y + y = 8 + 1

9x = 9

Dividing both sides of the equation by 9 gives us the value of x:

x = 1

Now we can substitute x = 1 into either of the original equations to find y. Let's substitute it into the first equation:

4(1) - y = 8

4 - y = 8

-y = 4

y = -4

Therefore, the solution to the system of equations is (1, -4), which corresponds to option A.