True or false, A solution of a system of linear equations is an ordered pair that satisfies one of the equations in the system?

The solution of a system of linear equations is an ordered pair that satisfies ALL the equations in the system.

What is the solution to the opening sentence? 3y -4 = y + 10

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True. A solution of a system of linear equations in two variables is an ordered pair that satisfies both equations in the system. It is the point of intersection between the two lines that represent the equations.

To determine if an ordered pair is a solution to a system of linear equations, you can substitute the values of the variables into each equation and check if both equations are true.

For example, let's consider the system of linear equations:
Equation 1: 2x + 3y = 7
Equation 2: 4x - y = 8

To check if the ordered pair (1, 2) is a solution to the system, substitute x = 1 and y = 2 into both equations:
Equation 1: 2(1) + 3(2) = 7
Simplifying, we get: 2 + 6 = 7, which is not true.

Equation 2: 4(1) - 2 = 8
Simplifying, we get: 4 - 2 = 8, which is also not true.

Since the ordered pair (1, 2) does not satisfy both equations, it is not a solution to the system of linear equations.