If the coordinates of a point are (x, y) such that x + y = 10 and x - y = 2, wha

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Question: If the coordinates of a point are (x, y) such that x + y = 10 and x - y = 2, what are the coordinates of the point?

Options:

Correct Answer: (6, 4)

Solution:

Solving the equations x + y = 10 and x - y = 2 simultaneously gives x = 6 and y = 4.

If the coordinates of a point are (x, y) such that x + y = 10 and x - y = 2, what are the coordinates of the point?

If the coordinates of a point are (x, y) such that x + y = 10 and x - y = 2, what are the coordinates of the point?

Step 1: Write down the two equations: x + y = 10 and x - y = 2.
Step 2: From the second equation (x - y = 2), solve for x: x = y + 2.
Step 3: Substitute the expression for x (from Step 2) into the first equation: (y + 2) + y = 10.
Step 4: Simplify the equation: 2y + 2 = 10.
Step 5: Subtract 2 from both sides: 2y = 8.
Step 6: Divide both sides by 2: y = 4.
Step 7: Now that we have y, substitute y back into the expression for x: x = 4 + 2.
Step 8: Calculate x: x = 6.
Step 9: The coordinates of the point are (x, y) = (6, 4).

Simultaneous Equations – The question tests the ability to solve two linear equations simultaneously to find the values of the variables.
Coordinate Geometry – The question involves understanding the relationship between algebraic equations and their graphical representation in a coordinate system.