Final answer:
To solve a system of equations using elimination, multiply each equation by an appropriate number to eliminate one variable when adding or subtracting the equations. After finding one variable, substitute it back into one of the original equations to solve for the other. Finally, check the solution to ensure it's correct.
Step-by-step explanation:
To solve a system of equations using elimination, we aim to cancel one of the variables by combining the two equations. For example, if the equations are set up in a way that allows the coefficients of one of the unknowns to be opposites when multiplied by appropriate numbers, those terms will cancel out when the equations are added together, leaving a new equation with a single variable.
Two recommended strategies for using elimination might include:
- Multiplying the first equation by a number that would make the coefficients of one of the variables the same (or opposites) as the coefficients in the second equation.
- Multiplying the second equation accordingly so that when you add or subtract the equations, one variable is eliminated.
In the given example, if we utilize the proper constants for multiplication, we will arrive at a situation where adding or subtracting the two modified equations will leave us with an equation in one variable. This can then be solved algebraically, thereby finding the value for one of the unknowns. Once we have one unknown, we can substitute it back into one of the original equations to find the value of the other variable.
Once we find a potential solution, as indicated — the system has exactly one solution which is (0, -3) — we must then check that the solution satisfies both of the original equations. If it does, this confirms the solution is reasonable and correct.