Solving Systems of Equations

The video tutorial explains how to find the value of an expression involving two equations: X + Y = 4 and X - Y = 3. Initially, it demonstrates solving the system of equations to find X and Y, then substituting these values into the expression. However, it introduces a more efficient method by recognizing the expression as a difference of squares, allowing for direct substitution of known values, leading to a quicker solution. The final value of the expression is calculated as 48.

What are the given equations in the problem?

• X + Y = 3 and X - Y = 4

• X + Y = 5 and X - Y = 2

• X + Y = 6 and X - Y = 1

• X + Y = 4 and X - Y = 3

What is the first step in solving the system of equations traditionally?

• Divide the equations by 2

• Subtract the equations to eliminate X

• Add the equations to eliminate Y

• Multiply both equations

After eliminating Y, what is the value of X?

• X = 3

• X = 4

• X = 7/2

• X = 5

What mathematical property is used to simplify the expression in the efficient method?

• Quadratic formula

• Difference of squares

• Sum of cubes

• Pythagorean theorem

What is the final value of the expression using the efficient method?

• 54

• 48

• 42

• 36