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- When an equation has two variables, the set of ordered pairs that are the solution to the equation are called the solution set to the equation.
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When an equation has two variables, the set of ordered pairs that are the solution to the equation are called the solution set to the equation. In this tutorial, you'll learn the definition of a solution set and see an example. Take a look!
- What is an Ordered Pair
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- What is an Ordered Pair
In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities . For example, for a set of polynomials over a ring , the solution set is the subset of on which the polynomials all vanish (evaluate to 0), formally.
Sep 17, 2022 · This vector equation is called the parametric vector form of the solution set. Since x3 and x4 are allowed to be anything, this says that the solution set is the set of all linear combinations of ( 8 − 4 1 0) and ( 7 − 3 0 1) . In other words, the solution set is. Span{( 8 − 4 1 0), ( 7 − 3 0 1)}.
Nov 16, 2022 · Example 1 Show that each of the following numbers are solutions to the given equation or inequality. x = 3 x = 3 in x2 −9 = 0 x 2 − 9 = 0. y = 8 y = 8 in 3(y+1) =4y−5 3 ( y + 1) = 4 y − 5. z = 1 z = 1 in 2(z−5) ≤ 4z 2 ( z − 5) ≤ 4 z. z = −5 z = − 5 in 2(z−5) ≤ 4z 2 ( z − 5) ≤ 4 z.
Solution Sets. Solution Sets for Equations. The set containing all the solutions of an equation is called the solution set for that equation. If an equation has no solutions, we write ∅ for the solution set. ∅ means the null set (or empty set). Equation.
The solution set: for fixed b , this is the set of all x such that Ax = b . This is a span if b = 0, and it is a translate of a span if b B = 0 (and Ax = b is consistent). It is a subset of R n . It is computed by solving a system of equations: usually by row reducing and finding the parametric vector form.
Jul 27, 2023 · In the first case, the solution set is a point on the number line, in the third case the solution set is the whole number line. Lets examine similar situations with larger matrices. [1.] (6 0 0 2)(x y) = (12 6), one solution: (2 3) [2b.] (1 3 0 0)(x y) = (4 1), no solutions.
