Understanding Simultaneous Equations

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What are simultaneous equations?

Simultaneous equations are a set of equations with multiple variables that are solved together.

What is the substitution method for solving simultaneous equations?

The substitution method involves solving one equation for one variable, then substituting that expression into the other equation.

How does the elimination method work?

The elimination method involves adding or subtracting equations to eliminate one of the variables.

What is the graphical method of solving simultaneous equations?

The graphical method involves plotting each equation on a graph and identifying the intersection point.

What does it mean if two lines on a graph are parallel when solving simultaneous equations?

If two lines are parallel, it means the equations have no solution because they never intersect.

What does it mean if two lines coincide on a graph?

If two lines coincide, it means the equations are dependent and have infinitely many solutions.

How do you recognize a consistent system of equations?

A consistent system has at least one solution where the lines intersect at a point or coincide.

How do you recognize an inconsistent system of equations?

An inconsistent system has no solution, typically represented by parallel lines that never intersect.

What are linear simultaneous equations?

Linear simultaneous equations are equations of the first degree involving two or more variables solved together.

How can simultaneous equations be used in real-life scenarios?

Simultaneous equations can model real-life problems such as budgeting, mixture problems, and comparing rates.

What is the coefficient in a linear equation?

The coefficient is the numerical factor multiplied by a variable in an equation.

What do you do if one equation is already solved for a variable in the substitution method?

If one equation is solved for a variable, you can directly substitute that expression in the other equation.

How do you use addition in the elimination method?

To use addition in elimination, you add two equations to cancel out one variable after aligning their coefficients.

How can you check the solution of simultaneous equations?

Substitute the solution back into the original equations to verify each equation holds true.

What role does normalization play in the substitution method?

Normalization may involve manipulating one equation to simplify a variable, making substitution easier.

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