Question

The following system of equations has exactly one (x, y) pair for it'ssolution2x + 4y = 83x + y=9If we triple each side of the second equation, 3x +y =9, we have 9x + 3y = 27.Explain why the same (x, y) pair that is the solution to the system is also asolution to this new equation

Answer 1

Since we multiplied 3 to each side of the equation of 3x + y = 9, the new equation 9x + 3y = 27 pertains to the same equation. This means that the graph of 3x + y = 9 and 9x + 3y = 27 are the same.

Thus, the intersection of 2x + 4y = 8 and 3x + y = 9 is the same as the intersection of 2x + 4y = 8 and 9x + 3y = 27.

Therefore, the solution of 2x + 4y = 8 and 9x + 3y = 27 is the same solution as the first system of linear equation.