Solving a System of Simultaneous Equations

The video tutorial explains how to solve simultaneous equations by manipulating them to have the same unknowns, either x or y. It emphasizes the importance of showing clear algebraic working to earn full marks. The process involves doubling one equation to match the y values, then adding or subtracting the equations to eliminate y and solve for x. Once x is found, it is substituted back into one of the original equations to find y. The tutorial concludes by explaining the marks allocation for each step.

Why is it important to show clear algebraic working when solving simultaneous equations?

• To ensure the answer is correct

• To earn all available marks

• To confuse the examiner

• To make the solution look neat

What is the first step in solving simultaneous equations by manipulation?

• Subtract the equations

• Add the equations together

• Solve for x directly

• Make the unknowns the same

How do you make the y values the same in both equations?

• Multiply the top equation by 3

• Multiply the bottom equation by 2

• Multiply the top equation by 2

• Add 4 to both equations

What operation is performed to eliminate the y variable?

• Add the equations

• Subtract the equations

• Multiply the equations

• Divide the equations

After eliminating y, what is the next step to find the value of x?

• Divide by the coefficient of x

• Add 10 to both sides

• Subtract 32 from both sides

• Multiply by 16

Once x is found, what should be done next?

• Multiply x by 2

• Solve for another variable

• Substitute x back into one of the original equations

• Add x to both equations

What is the final value of y when x is substituted back into the equation?

• 4

• 3

• 5

• 4.5