Question

Solve first by elimination using graphs of the two equations, then by elimination. In case, be prepared to explain what the result tells about solutions for the system and how the result is demonstrated in the graph and in the algebraic solution process.

OPTION 1: Graphical representation and elimination method.
OPTION 2: Graphical representation and substitution method.
OPTION 3: Substitution method and addition method.
OPTION 4: Addition method and graphical representation.

Answer 1

To solve simultaneous equations, one can use graphical representation, elimination, or substitution methods. Analytical techniques like elimination or substitution are typically more accurate than graphs. After solving, check by plugging the solution back into the original equations.

Step-by-step explanation:

To solve the simultaneous equations for the unknowns using different methods, such as elimination, substitution, and graphical representation, we first need to identify the knowns (the coefficients and constants in the equations) and the unknowns (the variables we need to solve for).

Option 1 involves using a graphical representation to visualize where the lines intersect, which corresponds to the solution of the system. However, using an analytical technique such as elimination or substitution is often more accurate, as it does not rely on the scale or precision of the graph.

For elimination, we manipulate the equations to cancel out one variable, allowing us to solve for the other. In substitution, we solve one equation for one variable and substitute it into the other equation to find the remaining variable. These methods yield exact numerical solutions.

Finally, checking the solution involves substituting the values back into the original equations to ensure they satisfy both. If the calculations are correct, the solution is deemed reasonable.