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?
Infinitely many solutions.
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.
(II): 3y= -2.5x+12
(II): Remove parentheses
(II): Subtract term