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kent davidge
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The set of equations $$A = a_1 x + a_2y$$ ¨$$B = b_1 x + b_2 y$$ can be solved for the unkowns ##x## and ##y##. Does it make sense to have ##x## and ##y## be known and instead ##A## and ##B## unkown?
kent davidge said:Does it make sense to have ##x## and ##y## be known and instead ##A## and ##B## unknown?
Sorry for not clarifying, I was regarding them as unkowns. Otherwise the solution would be obvious as @BvU pointed out.Stephen Tashi said:What would ##a_1, a_2,b_1,b_2## be? Known or unknown?
A solution to a system of equations is a set of values that make all of the equations in the system true when substituted into the variables. In other words, it is the point or points where all of the equations intersect on a graph.
There are several methods for solving a system of equations, including substitution, elimination, and graphing. Each method involves manipulating the equations in the system to isolate a variable and solve for its value. The final step is to check the solution by plugging it back into the original equations.
A consistent system of equations has at least one solution, meaning the equations intersect at one or more points. An inconsistent system has no solutions, meaning the equations are parallel and never intersect. This can be seen on a graph as either overlapping lines or parallel lines.
Yes, a system of equations can have infinitely many solutions. This occurs when the equations are equivalent, meaning they represent the same line. In this case, any point on the line is a solution to the system. On a graph, this would appear as two lines overlapping perfectly.
Systems of equations can be used to model and solve real-life problems, such as determining the optimal number of items to produce to maximize profit or finding the best combination of ingredients for a recipe. They can also be used to solve problems involving rates, proportions, and other mathematical relationships.