Final answer:
The question asks to verify if ordered pairs are solutions to given linear equations by substituting and checking the resulting values. The ordered pairs were tested accordingly, providing clarity for each case, with (3,1) and (1,3) as solutions, but (2,0) is only a solution to one of the two system equations and also to y = -3x + 6.
Step-by-step explanation:
The subject's question involves determining whether given ordered pairs are solutions to systems of linear equations. An ordered pair is a solution to a system of equations if, when the x and y values are substituted into each equation, the equations are true. Let's test the ordered pairs for each given equation:
- (3,1); x + y = 4: Substitute x with 3 and y with 1 to get 3 + 1, which equals 4. Since this matches the equation, the ordered pair (3,1) is a solution.
- (1,3); x - y = -2: Substitute x with 1 and y with 3 to get 1 - 3, which equals -2. Thus, (1,3) is also a solution.
- For the system composed of two equations, y = x - 2 and 2x - y = 3, the ordered pair (2,0) is tested: For the first equation, substitute x with 2 to get y = 2 - 2, which gives y = 0, and for the second equation, 2(2) - 0 = 4, which does not equal 3, so (2,0) is not a solution.
- y = -3x + 6: If the ordered pair (2,0) is a solution when x is 2, y should be -3(2) + 6, which is 0. Thus, (2,0) is a solution to this equation.
For each case, we use the definition of linear equations and the properties of solutions to systems of equations to determine the truth of the statements.