Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are asked to solve the following system of linear equations: $8x - 4y = 6$ $12x - 6y = 9$ If ther...

Linear EquationsSystems of EquationsSolution SetsDependent System
2025/3/19

We are asked to solve the following system of equations: $x + 2y = 2$ $3x + 6y = 8$ If the system ha...

Systems of EquationsLinear EquationsElimination MethodContradiction
2025/3/19

The problem asks us to express $\frac{3\sqrt{2}-\sqrt{3}}{2\sqrt{3}-\sqrt{2}}$ in the form $\frac{\s...

RadicalsRationalizationSimplificationFractions
2025/3/19

We are asked to solve the system of equations: $ \begin{cases} -4x + 3y = -9 \\ 3x - 2y = 8 \end{cas...

Systems of EquationsLinear EquationsElimination Method
2025/3/19

The problem asks to express the fraction $\frac{3\sqrt{2} - \sqrt{3}}{2\sqrt{3} - \sqrt{2}}$ in the ...

RadicalsSimplificationRationalizationFractions
2025/3/19

The first problem asks us to express the fraction $\frac{3\sqrt{2} - \sqrt{3}}{2\sqrt{3} - \sqrt{2}}...

RadicalsSimplificationEquationsRationalizationSquare Roots
2025/3/19

We are asked to find the equation of a line with slope $m = \frac{3}{5}$ that passes through the poi...

Linear EquationsSlope-intercept formPoint-slope form
2025/3/19

The problem consists of three parts: 1. Graph the inequality $3x + 4y < 24$ and shade the unwanted ...

Linear InequalitiesFunctionsLinear EquationsSlope-intercept formPoint-slope form
2025/3/19

The problem gives the function $f(x) = 3x - 12$. Part I asks us to determine the value of $f(5)$. P...

FunctionsLinear FunctionsEvaluating FunctionsSolving Equations
2025/3/19

We are given a system of two equations with two variables, $x$ and $y$: $4x - 2y = 20$ $x - 2y = -10...

Linear EquationsY-interceptCoordinate Geometry
2025/3/19