2. Solving Systems Using Substitution
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What does it mean when solving a system of equations results in an identity or a contradiction?
No solution.
To determine how many solutions this system has, we will solve it by substitution. Doing so will result in one of three cases.
Result of solving by substitution | Number of solutions |
---|---|
A value for x and y is determined. | One solution |
An identity is found, such as 2=2. | Infinitely many solutions |
A contradiction is found, such as 2≠3. | No solution |
When solving a system of equations using substitution, there are three steps.
(I): 11y= 14-12x
(I): Remove parentheses
(I): Add terms