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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.
These toys are sold to stores in boxes. The total weight of the content of each box is of 20 kilograms. Each robot weighs 54 kilogram and each car weighs 101 kilogram. If x is the number of robots and y the number of cars in a box, the given information can be expressed by a linear equation.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.
The price of gold is about $2000 per ounce, while the price of of silver is about $25 per ounce. The vlogger spent a total of $7075 in both silver and gold. Let g and s be the ounces of gold and silver, respectively, that the vlogger bought. Then, the given information can be modeled by a linear equation.(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.
As part of his student council duties, Tadeo is in charge of getting equipment for the school gym. At the moment, the gym needs new basketballs and volleyballs. Each basketball costs $75 and each volleyball costs $50. The gym's budget is $1400.
Tadeo can only go to the store once to buy the equipment. Each basketball weighs 22 ounces and each volleyball weighs 10 ounces. The total weight of the purchased balls is 364 ounces. For Tadeo to be able to spend all the budget in one go, the number of basketballs b and volleyballs v need to satisfy the following system of linear equations.