Simultaneous Equations

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What does it mean if two lines coincide in simultaneous equations?

If two lines coincide, there are infinitely many solutions as they represent the same line.

How do you solve the equations: $2x + 3y = 12$ and $x - y = 1$ using substitution?

Solve $x$ from the second equation: $x = y + 1$. Substitute into the first: $2(y + 1) + 3y = 12$. Solve for $y$, then find $x$.

How do you apply the elimination method to $3x + 2y = 16$ and $5x - 2y = 4$?

Add the equations: $(3x + 2y) + (5x - 2y) = 16 + 4$. This simplifies to $8x = 20$, so $x = 2.5$. Substitute back to find $y$.

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