Question

1. determine if the ordered pair is a solution to the system. show all work.

ordered pair: \\((1, -3)\\)

system: \\(\\{2x - y = 5 \quad y = 7x - 4\\)\\)

1. for each equation, identify the slope and the y-intercept. then sketch each on the coordinate plane provided.

a. \\(y = -\frac{1}{2}x + 5\\)

y-int = ____ \quad slope = ____

b. the line passing through \\((0, 7)\\) and \\((5, 1)\\).

Explanation:

Check the first equation of the system

Using the System of Equations knowledge point

$$
LATEXBLOCK0
$$

Check the second equation of the system

Using the System of Equations knowledge point

$$
LATEXBLOCK1
$$

Since the ordered pair does not satisfy both equations, it is not a solution.

Find slope and y-intercept for equation 5a

Identify parameters from the slope-intercept form \(y = mx + b\).

• The equation is \(y = -\frac{1}{2}x + 5\).
• The slope \(m\) is the coefficient of \(x\), which is \(-\frac{1}{2}\).
• The y-intercept \(b\) is the constant term, which is \(5\) (or the point \((0, 5)\)).

Find slope and y-intercept for equation 5b

Using the Linear Equations Solving knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question 4

No, the ordered pair \((1, -3)\) is not a solution to the system.

Work:

1. Substitute into the first equation:

$$2(1) - (-3) = 2 + 3 = 5 \quad (\text{True})$$

1. Substitute into the second equation:

$$-3 = 7(1) - 4 \implies -3 = 3 \quad (\text{False})$$

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Question 5a

• y-int = \(5\)
• slope = \(-\frac{1}{2}\)

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Question 5b

• y-int = \(7\)
• slope = \(-\frac{6}{5}\)