NY Regents Algebra I Systems of Linear Equations — practice questions

1. The definition states directly that grouping two or more linear equations together forms a system of linear equations. 2. A quadratic equation, a compound inequality, and a linear function are all different mathematical objects, none of which describes a group of linear equations. 3. Most algebra courses focus on systems of exactly two linear equations in two unknowns, though larger systems are possible too. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_

1. Substitute x = 2 and y = -1 into 3x - y = 7: 3(2) - (-1) equals 6 plus 1, which equals 7, a true statement. 2. Substitute the same values into x - 2y = 4: 2 - 2(-1) equals 2 plus 2, which equals 4, also a true statement. 3. Since the pair makes both equations true, it is a solution to the system. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_

1. Substitute x = 3 and y = 2 into 3x - y = 7: 3(3) - 2 equals 9 minus 2, which equals 7, a true statement. 2. Substitute the same values into x - 2y = 4: 3 - 2(2) equals 3 minus 4, which equals -1, not 4, a false statement. 3. Since the pair fails the second equation, it is not a solution to the system, even though it satisfies the first. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_