Linear Equations and Systems of Linear Equations

A linear function of x is graphed on a coordinate grid. The points (6, 34) and (18, 26) lie on the graph of the function. What are the rate of change of the function and the value of the function when x = 24?

A system of two linear equations is represented by the graph. Which statement about the solution of the systems of equations is true?

• (0, 0) is the only solution.

• (3, 2) is the only solution.

• (0, 0) and (3, 2) are both solutions.

• (0, 0), (0, 6), and (3, 2) are all solutions.

Determine which of the following ordered pairs would satisfy the given system of linear equations in two variables.

• (1, 2)

• (0, 2)

• (-1, 3)

• (3, 1)

Which of the following is true about the system of linear equations in two variables?

I. Any set of linear equations.

II. A set of two or more linear equations in two variables.

III. A system of linear equations may have only one solution, infinitely many solutions, or no solution at all.

IV. A system of linear equations in two variables can be solved algebraically or graphically.

What system of linear equations in two variables is equivalent to (see figure 1)?

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What system of linear equations in two variables is the same as (see photo).

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Which of the following ordered pair satisfies the given system (see photo).

• (7, 4)

• (-7, -4)

• (7, -4)

• (-7, 4)

What is the value of k in the system (see photo) satisfies both equations in the system?

• -1 and 1

• -2 and 2

• -3 and 3

• -4 and 4

Jayda was tasked by her teacher to verify if the ordered pair (—1, 2) will satisfy to the system (see photo). Is her solution correct?

• Yes, because she substituted the values of the variable x = 1 and y = -2.

• Yes, because she followed the process of evaluating the system of linear equations.

• No, because the point (-1, 2) is not a common point of the given system of linear equations in two variables.

• No, because she is supposed to make two false statements that makes a solution of the system of linear equations.

What system of linear equations in two variables is equivalent to (see photo).

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