Question

Find a pair of numbers that is a member of both -2y + 3x = 5 and 5y + 3x = -23.

Options:
Option 1: (4, -6)
Option 2: (1, -10)
Option 3: (-2, 7)
Option 4: (3, -8)

Answer 1

To find a pair of numbers that is a member of both -2y + 3x = 5 and 5y + 3x = -23, solve the system of equations by substituting and simplifying.The pair of numbers that satisfies both equations is (-1, -4).

Step-by-step explanation:

To find a pair of numbers that is a member of both -2y + 3x = 5 and 5y + 3x = -23, we can solve the system of equations simultaneously.

Step 1: Choose one equation and solve for one variable in terms of the other. Let's choose -2y + 3x = 5 and solve for x:

x = (5 + 2y) / 3

Step 2: Substitute the value of x in terms of y into the other equation. Let's substitute x = (5 + 2y) / 3 into 5y + 3x = -23:

5y + 3((5 + 2y) / 3) = -23

Step 3: Simplify and solve for y:

5y + 5 + 2y = -23

7y = -28

y = -4

Step 4: Substitute the value of y into the equation x = (5 + 2y) / 3 to find x:

x = (5 + 2(-4)) / 3

x = -1

Therefore, the pair of numbers that satisfies both equations is (-1, -4).