The problem asks us to identify which of the given ordered pairs $(x, y)$ satisfy the equation $y = -3x$.

AlgebraLinear EquationsCoordinate GeometryEquation Solving
2025/5/12

1. Problem Description

The problem asks us to identify which of the given ordered pairs (x,y)(x, y) satisfy the equation y=3xy = -3x.

2. Solution Steps

To determine if an ordered pair (x,y)(x, y) satisfies the equation y=3xy = -3x, we substitute the xx and yy values into the equation and check if the equation holds true.
* (6, 4): y=3x4=3(6)4=18y = -3x \Rightarrow 4 = -3(6) \Rightarrow 4 = -18. This is false.
* (-2, 6): y=3x6=3(2)6=6y = -3x \Rightarrow 6 = -3(-2) \Rightarrow 6 = 6. This is true.
* (3, 1): y=3x1=3(3)1=9y = -3x \Rightarrow 1 = -3(3) \Rightarrow 1 = -9. This is false.
* (-6, -4): y=3x4=3(6)4=18y = -3x \Rightarrow -4 = -3(-6) \Rightarrow -4 = 18. This is false.
* (2, -6): y=3x6=3(2)6=6y = -3x \Rightarrow -6 = -3(2) \Rightarrow -6 = -6. This is true.
* (-1, 3): y=3x3=3(1)3=3y = -3x \Rightarrow 3 = -3(-1) \Rightarrow 3 = 3. This is true.
Therefore, the ordered pairs that satisfy the equation are (-2, 6), (2, -6), and (-1, 3).

3. Final Answer

(-2, 6), (2, -6), (-1, 3)

Related problems in "Algebra"

The problem is divided into two parts. The first part asks to sketch the graph of the function $y = ...

Quadratic FunctionsGraphingInequalitiesLinear EquationsCoordinate GeometryVertex of a ParabolaMinimum Value
2025/6/17

The problem consists of two parts. Part 1: Convert the given matrix $\begin{bmatrix} 5 & -7 & 1 \\ 6...

Linear AlgebraMatricesDeterminantsMatrix Transformations
2025/6/17

The problem presents three separate mathematical questions: 1. Find a number that when multiplied b...

Linear EquationsWord ProblemsAge ProblemsRectangle Perimeter
2025/6/17

Sophat is 51 years old, and Rasmei is 21 years old. In how many years will Sophat be twice the age o...

Age ProblemsLinear EquationsWord Problems
2025/6/17

The problem consists of two parts. Part 1: Solve the equation $5(1 + 4e^{0.1x-1}) = 25$ for $x$. Par...

Exponential EquationsLogarithmic EquationsQuadratic EquationsLogarithm PropertiesEquation Solving
2025/6/17

The problem presents a formula for $a_n$, which is $a_n = a_1 \cdot r^{n-1}$. This is the formula fo...

Sequences and SeriesGeometric SequenceFormula
2025/6/17

The image contains several math problems. I will solve "Example 1" and "Related Problem 1". Example ...

SequencesSeriesSummationArithmetic SeriesFormula Derivation
2025/6/17

The problem consists of two questions. Question 1 asks to evaluate several expressions involving exp...

ExponentsRadicalsAlgebraic ExpressionsEquation Solving
2025/6/17

We need to evaluate the expression: $(\frac{-5\sqrt{2}}{\sqrt{6}})(\frac{-\sqrt{7}}{3\sqrt{22}})$.

SimplificationRadicalsRationalizationFractions
2025/6/17

Simplify the expression $-6\sqrt{\frac{3y^2}{16}}$.

SimplificationRadicalsAbsolute ValueExponents
2025/6/17