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The problem asks us to identify which of the given ordered pairs are solutions to the equation $4y = 5 - 3x$. The graph of the equation is also given.

AlgebraLinear EquationsCoordinate GeometrySolutions of EquationsOrdered Pairs
2025/5/12

1. Problem Description

The problem asks us to identify which of the given ordered pairs are solutions to the equation 4y=5−3x4y = 5 - 3x. The graph of the equation is also given.

2. Solution Steps

We can check each ordered pair by substituting the xx and yy values into the equation and seeing if it holds true. Alternatively, we can see if the points lie approximately on the plotted line.
* (3, -1): 4(−1)=5−3(3)⇒−4=5−9⇒−4=−44(-1) = 5 - 3(3) \Rightarrow -4 = 5 - 9 \Rightarrow -4 = -4. This is true.
* (7, -4): 4(−4)=5−3(7)⇒−16=5−21⇒−16=−164(-4) = 5 - 3(7) \Rightarrow -16 = 5 - 21 \Rightarrow -16 = -16. This is true.
* (4, 3): 4(3)=5−3(4)⇒12=5−12⇒12=−74(3) = 5 - 3(4) \Rightarrow 12 = 5 - 12 \Rightarrow 12 = -7. This is false.
* (5, -7): 4(−7)=5−3(5)⇒−28=5−15⇒−28=−104(-7) = 5 - 3(5) \Rightarrow -28 = 5 - 15 \Rightarrow -28 = -10. This is false.
* (-5, 5): 4(5)=5−3(−5)⇒20=5+15⇒20=204(5) = 5 - 3(-5) \Rightarrow 20 = 5 + 15 \Rightarrow 20 = 20. This is true.
* (-1, -3): 4(−3)=5−3(−1)⇒−12=5+3⇒−12=84(-3) = 5 - 3(-1) \Rightarrow -12 = 5 + 3 \Rightarrow -12 = 8. This is false.
Therefore, the ordered pairs that are solutions to the equation are (3, -1), (7, -4), and (-5, 5).

3. Final Answer

(3, -1), (7, -4), (-5, 5)

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