Is (x, y) a solution to the system of equations?

Learning Objectives Define a system of linear equations and its solution. Substitute the x and y values from an ordered pair into a linear equation. Evaluate a linear equation to verify if a given ordered pair makes the equation a true statement. Test an ordered pair in all equations of a two-variable linear system. Conclude with a definitive 'yes' or 'no' answer, supported by mathematical evidence, whether an ordered pair is a solution to the system. Explain why a point must satisfy all equations in a system to be considered a solution. Ever tried to find a location that's on two different streets at the same time? 🗺️ That single intersection point is like the solution to a system of equations! In this tutorial, you will learn a straightforward met...

TermDefinitionExample System of Linear EquationsA set of two or more linear equations that share the same variables.The set of equations { y = 3x - 2, x + y = 6 } is a system of linear equations. Ordered PairA pair of numbers, written as (x, y), that represents a specific point on a coordinate plane.(4, 1) is an ordered pair where x = 4 and y = 1. Solution to a Single EquationAn ordered pair that makes a single equation a true statement when its values are substituted for the variables.(3, 1) is a solution to 2x - y = 5 because 2(3) - 1 = 5, which simplifies to 5 = 5. Solution to a System of EquationsAn ordered pair that is a solution to EVERY equation in the system. Graphically, it is the single point where all the lines in the system intersect.(2, 4) is the solution to the system { y =...

The Substitution Principle To test a point (x₀, y₀) in an equation like Ax + By = C, replace every 'x' with x₀ and every 'y' with y₀. Then, evaluate if A(x₀) + B(y₀) = C. This is the fundamental process for checking if a point satisfies an equation. You are plugging in the given values to see if the equation remains balanced. The System Solution Criterion An ordered pair (x, y) is a solution to a system if and only if it produces a true statement for EVERY equation in the system. If the ordered pair fails to satisfy even one equation, it is not a solution to the system. There are no exceptions. It must work for all of them.