# Simultaneous Equations

- Simultaneous equations are a set of equations with multiple unknowns that are solved together.
- Two common methods to solve simultaneous equations are substitution and elimination.
- In the substitution method, the value of one variable from one equation is substituted into the other equation.
- In the elimination method, one variable is eliminated by adding or subtracting the equations, leaving an equation with only one variable.
- If the coefficients of one variable in both equations are the same, subtraction can be used to eliminate that variable.
- If the coefficients of one variable in both equations are the same but with opposite signs, addition can be used to eliminate that variable.
- If the coefficients of one variable are not the same, you may need to multiply one or both equations by a suitable number to make the coefficients the same before eliminating.
- Once one variable is found, this value is substituted into one of the original equations to find the value of the remaining unknown.
- Simultaneous equations can be used to solve problems in various real-life situations, such as calculating rates or costs.
- A pair of simultaneous equations may have one solution, no solutions, or infinitely many solutions.
- The graphical representation of simultaneous equations is the point of intersection of the lines that represent each equation. If two lines intersect, it means there’s a common solution for both equations.
- Note that if the lines do not intersect, it means the simultaneous equations have no solution. If the lines coincide, it means the equations have infinitely many solutions.
- In order to master solving simultaneous equations, consistent practice and understanding of the underlying concepts are important. This can be achieved through completing practice problems and seeking help when needed.