Week two concept check

Week two concept check - (b) A linear equation has no...

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(a) A linear equation has infinitely many solutions if, upon simplification, we end up with an algebraic identity. For example, consider 2x + 10 = 2(5 + x) 2x + 10 = 10 + 2x Canceling the 2x term on both sides, we end up with 10 = 10. (This is an identity since it is always true that 10 = 10) Therefore, the equation 2x + 10 = 2(5 + x) has infinite solutions (Any value assigned to x will satisfy the equation)
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Unformatted text preview: (b) A linear equation has no solution if, upon simplification, we end up with something which is mathematically false. For example, consider 3x - 5 = 3(5 + x) 3x - 5 = 15 + 3x Canceling the 3x term on both sides, we end up with -5= 15. (This is false) Therefore, the equation 3x - 5 = 15 + 3x has no solution (No value assigned to x will satisfy the equation)...
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