Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

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Resolver una ecuación de 1er grado sin fracciones

Resolver una ecuación de 1er grado sin fracciones

In this question the students have to solve a linear recurrence of order 2. The sequence is asked in recurrence form and the goal is to find its closed form.

Resolver una ecuación de 1er grado con fracciones

An economic dispatch problem with three generators. The steps help the students to solve this using lagrangian multipliers. This question is designed to allow students studying economic dispatch to practice solving the problem.

Simultaneous equations question. values for the coefficients are generated to be small numbers, random values are generated for the weights and the resultant energies are calculated for the question. Student needs to solve equations to find coefficients. Advice gives solution using method of elimination.

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

Simultaneous equation problem as circuit analysis to find unknown currents. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

Simultaneous equation problem as circuit analysis to find unknown voltages. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

The proportion of the sodium carbonate, $p$, which has dissolved by time $t$ seconds is given by the formula $ p=\frac{bt-at^2}{c}$. The aim is to calculate the proportion of sodium carbonate in a solution at a given time and vice versa.

The student must solve a pair of simultaneous equations in $x$ and $y$.

The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.

Given an equation with variable x in the power on two different bases, students must solve for x. Hints are included in the question to aid the student as needed.

Given an equation where x is the base of a log term, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation involving x as a power on e, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

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Solving an equation of the form $ax \equiv b\;\textrm{mod}\;n$ where $a$ and $n$ are coprime.

The students should solve a Blakley secret sharing scheme and find the secret.

This question asks students to solve a discrete logarithm problem with Pollard's rho algorithm as exposed in the book "introduction to cryptography with open source software" by McAndrew.

This question tests the student's ability to solve Integer Programming problems applying Population-based Metaheuristics.

This question tests the student's ability to solve Integer Programming problems applying Single State Metaheuristics.

This question tests the student's ability to model and solve Integer Programming problems by Branch and bound method

This question tests the student's ability to model and solve Integer Programming problems by Branch and bound method

This question tests the student's ability to solve Linear Programming problems by hand using the Simplex Method.

This question tests the student's ability to solve Linear Programming problems by hand using the Simplex Method.

This question tests the student's ability to model and solve Integer Programming problems