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(5, -2), or x = 5 and y = -2.

Step-by-step explanation:

We can solve the two equations algebraically by eliminating a variable:

2x + 5y = 0

3x - 4y = 23

Eliminate the x variable by finding the least common multiple and multiplying both equations:

3(2x + 5y = 0)

2(3x - 4y = 23)

Distribute and subtract the bottom equation from the top:

6x + 15y = 0

6x - 8y = 46

0x + 23y = -46

23y = -46

y = -2.

Plug in y into an equation to solve for x:

2x + 5(-2) = 0

2x - 10 = 0

2x = 10

x = 5. Therefore:

The solution to this equation is (5, -2), or x = 5 and y = -2.

x = 5; y = -2

Step-by-step explanation:

2x + 5y = 0

3x - 4y = 23

Let's eliminate y. Multiply the first equation by 4. Multiply the second equation by 5. Then add them.

         8x + 20y = 0

(+)      15x - 20y = 115

          23x         = 115

x = 5

Now we substitute 5 for x in the first equation and solve for y.

2(5) + 5y = 0

5y = -10

y = -2

Solution: x = 5; y = -2