Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are given a system of three equations with three variables $x$, $y$, and $z$: $3xy = 2(x+y)$ $5yz...

Systems of EquationsAlgebraic ManipulationVariable Transformation

We are asked to solve the system of linear equations: $x + y = a$ $y + z = b$ $z + x = c$

Linear EquationsSystems of EquationsSolving Equations

We are given a system of equations: $\frac{xy}{ay+bx} = \frac{1}{c}$ $\frac{yz}{bz+cy} = \frac{1}{a}...

System of EquationsAlgebraic Manipulation

The problem asks: A pole is buried in the ground by one-third of its length. Half of its length is i...

Linear EquationsWord ProblemFractions

The problem asks us to solve the given systems of equations. We will solve system (a). The system is...

Systems of EquationsLinear EquationsSolving Equations

Solve for $x$ in the equation: $\frac{x-a}{bc} + \frac{x-b}{ac} + \frac{x-c}{ab} = 2(\frac{1}{a} + \...

EquationsAlgebraic ManipulationVariablesSolving Equations

The problem asks to solve the given equations for the unknown variable $x$ and discuss the solution ...

EquationsLinear EquationsQuadratic EquationsVariable SolvingParameter AnalysisSolution DiscussionAlgebraic Manipulation

We need to solve the equation $\frac{a-x}{b-a} - \frac{a+x}{a+b} = \frac{2ax}{a^2 - b^2}$ for $x$ in...

Equation SolvingLinear EquationsFractional EquationsVariable Isolation

Solve the equation $\frac{(x^2+a^2-b^2)(a+x)}{ax} + \frac{(a^2+b^2-x^2)(b+a)}{ab} + \frac{(b^2+x^2-a...

EquationsAlgebraic ManipulationQuadratic FormulaPolynomial Equations

The problem asks us to construct the graphs of the following linear functions: a) $y = 2x - 1$ b) $y...

Linear FunctionsGraphingCoordinate Geometry

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