The problem asks to identify which ordered pairs (x, y) satisfy the equation $-4x + 3y = 0$. We need to test each given ordered pair in the equation and select the ones that make the equation true.

AlgebraLinear EquationsCoordinate GeometrySolutions
2025/5/12

1. Problem Description

The problem asks to identify which ordered pairs (x, y) satisfy the equation 4x+3y=0-4x + 3y = 0. We need to test each given ordered pair in the equation and select the ones that make the equation true.

2. Solution Steps

We will substitute the x and y values of each ordered pair into the equation 4x+3y=0-4x + 3y = 0 and check if the equation holds true.
* (3, 0): 4(3)+3(0)=12+0=120-4(3) + 3(0) = -12 + 0 = -12 \ne 0.
So (3, 0) is not a solution.
* (0, 0): 4(0)+3(0)=0+0=0-4(0) + 3(0) = 0 + 0 = 0.
So (0, 0) is a solution.
* (3, 4): 4(3)+3(4)=12+12=0-4(3) + 3(4) = -12 + 12 = 0.
So (3, 4) is a solution.
* (4, -3): 4(4)+3(3)=169=250-4(4) + 3(-3) = -16 - 9 = -25 \ne 0.
So (4, -3) is not a solution.
* (-3, 4): 4(3)+3(4)=12+12=240-4(-3) + 3(4) = 12 + 12 = 24 \ne 0.
So (-3, 4) is not a solution.
* (-3, -4): 4(3)+3(4)=1212=0-4(-3) + 3(-4) = 12 - 12 = 0.
So (-3, -4) is a solution.

3. Final Answer

The ordered pairs that represent points on the graph of the equation are:
(0, 0), (3, 4), (-3, -4)

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