Simple C++ program to solve 2 variable systems of equations using elimination method.

SolveSystemsOfEquations.cpp

// SystemsOfEquations.cpp : This file contains the 'main' function. Program execution begins and ends there.
//

#include <iostream>

struct Equation
{
	double xCoefficent;
	double yCoefficent;
	double result;
};

struct Equations
{
	Equation eq1;
	Equation eq2;
};

struct Answer
{
	double x;
	double y;
	bool solved = false;
};

// Solve systems of equations by elimination
Answer SystemsOfEquationsSolver(const Equations equ)
{
	Answer answer;

	// Determine a value to multiply equation 2 by which will eliminate
	// the y coefficients when the equations are added together
	// So we're doing 50.2 / 0.55 = 91.2727, then we're negating it
	const auto eliminator = -(equ.eq1.yCoefficent / equ.eq2.yCoefficent);
	// We're going to multiply equation 2 by this value which will yield
	// -91.2727 * 2.1x + -91.2727 * 0.55y = -91.2727 * 5.9
	// -191.6727X      + -50.2y           = -538.5090
	//                   ^^^^^^
	// See what I did there? Now y is gone when we add this to equation1,
	// that's why I call it the eliminator

	// Add them:
	//       3.4x +  50.2y =   44.5
	// -191.6727x + -50.2y = -538.5090
	// _________________________________
	// -188.2727x +     0y = -494.009090

	// Add the x's after multiplying by the eliminator yields -188.2727x
	const auto XSum = equ.eq2.xCoefficent * eliminator + equ.eq1.xCoefficent;

	// Add the results after multiplying by the eliminator yields -494.009090
	const auto ResultSum = equ.eq2.result * eliminator + equ.eq1.result;

	// After eliminating y, equation 2 now is:
	// -188.2727x = -494.009090
	// Divide both sides by the x coefficient -188.2727 to solve for x
	// x = 2.6239
	const auto x = ResultSum / XSum;

	// Ok, now we know X so plug it into our original equation 2 (or 1)
	// As a reminder, equation 2 is:
	//        2.1x + 0.55y =  5.9
	// So substituting in our x value:
	//        2.1 * 0.33459 + 0.55y = 5.9
	// Simplifies to:
	//         0.70265 + 0.55y = 5.9
	// Plug the solved x back into equation 2 and multiply by its coefficient
	const auto x2 = equ.eq2.xCoefficent * x;  // 2.1 * 2.6239 = 0.70265

	// Subtract x from both sides to eliminate the constant
	// 0.55y = 5.9 - (2.1 * 0.33459)
	// 0.55y = 0.38980
	const auto val = equ.eq2.result - x2;

	// Divide by 0.55 to isolate y
	// y = 0.38980 / 0.55
	// y = 0.7087
	const auto y = val / equ.eq2.yCoefficent;

	// Package the results and send them home
	answer.x = x;
	answer.y = y;
	answer.solved = true;
	return answer;
}

int main()
{
	const Equation equ1 = { 3.4, 50.2, 44.5 };
	const Equation equ2 = { 2.1, 0.55, 5.9 };
	const Equations equations
	{
		equ1, equ2
	};

	std::cout << "Solving: " << equ1.xCoefficent << "X + " << equ1.yCoefficent << "Y = " << equ1.result << "\n";
    	std::cout << "And:     " << equ2.xCoefficent << "X + " << equ2.yCoefficent << "Y = " << equ2.result << "\n";
	const auto answer = SystemsOfEquationsSolver(equations);
	std::cout << "The solution is: x = " << answer.x << " y = " << answer.y << "\n";

	// Test results
	std::cout << "Testing Solution 3.4 * " << answer.x << " + 50.2 * " << answer.y <<
		" = " << answer.x * 3.4 + answer.y * 50.2 << "\n";

	std::cout << "Testing Solution 2.1 * " << answer.x << " + 0.55 * " << answer.y <<
		" = " << answer.x * 2.1 + answer.y * 0.55 << "\n";

	return 0;
}