When solving equations with two unknowns, you need a system of equations. One equation with two variables has infinitely many solutions, represented as a line on a graph. Two independent equations create a system where the solution is the intersection point of the two lines.
The substitution method is one way to solve a system of two equations. First, solve one equation for one variable in terms of the other. Then substitute this expression into the second equation. This gives you one equation with one unknown, which you can solve. Finally, substitute back to find the other variable and check your solution.
The elimination method works by adding or subtracting equations to eliminate one variable. First, multiply one or both equations so that one variable has opposite coefficients. Then add the equations together to eliminate that variable. Solve for the remaining variable, substitute back to find the other, and check your solution.
The graphing method involves plotting both equations on the same coordinate system. Each equation represents a line, and the point where these lines intersect is the solution to the system. This method provides a visual understanding of the solution but may be less precise when the intersection point has non-integer coordinates.
To summarize, solving equations with two unknowns requires a system of two independent equations. You can use substitution, elimination, or graphing methods. Substitution works well when one equation is easily solved for a variable. Elimination is efficient when coefficients align well. Graphing provides visual insight but may be less precise. Always verify your solution by substituting back into both original equations.