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Here are a few recommended readings before getting started with this lesson.
Maya is researching a toy factory that currently produces robot action figures and car toys.
In a system of equations, an equivalent system can be created by replacing one equation with the sum of two or more equations in the system or by replacing an equation with a multiple of itself. An equation can be also replaced by the sum of that equation and a multiple of another equation in the system.
Remove parentheses
Commutative Property of Addition
Add and subtract terms
For each system of linear equations, verify whether the coordinate pair is a solution.
A vlogger that Diego likes to watch bought silver and gold to make Olympic-style medals. The vlogger will show the process of making the medals as a multi-video series.
(I): LHS/25=RHS/25
(I): Write as a sum of fractions
(II): LHS/5=RHS/5
(II): Write as a difference of fractions
(I), (II): ca⋅b=ca⋅b
(I), (II): Calculate quotient
(I), (II): Identity Property of Multiplication
(I): LHS−80g=RHS−80g
(II): LHS+10g=RHS+10g
Looking at the graph, it can be seen that the solution is about 3 ounces of gold and a bit more than 40 ounces of silver. In this case, since the point of intersection is not a lattice point, finding the exact solution is not possible.
(II): LHS/5=RHS/5
(II): Write as a difference of fractions
(II): ca⋅b=ca⋅b
(II): Calculate quotient
(II): Identity Property of Multiplication
(II): LHS+10g=RHS+10g
(I): s=10g+13
(I): LHS/5=RHS/5
(I): Write as a sum of fractions
(I): ca⋅b=ca⋅b
(I): Calculate quotient
(I): Subtract (II)
(I): Distribute -1
(I): Add and subtract terms
(I): LHS/450=RHS/450
Concept | Definition |
---|---|
Consistent System | A system of equations that has at least one solution. |
Inconsistent System | A system of equations that has no solution. |
Dependent System | A system of equations with infinitely many solutions. |
Independent System | A system of equations that has exactly one solution. |
Since the system has exactly one solution, it is both consistent and independent.