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belka [17]
2 years ago
8

Analyze the solution set of the following system by following the given steps. 2x + y = 5 3y = 9 − 6x Write each equation in slo

pe-intercept form. y = -2 x + 5 y = -2 x + 3 What do the equations have in common? How are they different?
Mathematics
1 answer:
Ulleksa [173]2 years ago
8 0

Step-by-step explanation:

Given the following systems of linear equations, 2x + y = 5, and 3y = 9 − 6x

<h2>Write each equation in slope-intercept form. </h2>

The slope-intercept form is: y = mx + b, where m = slope, and b = y-intercept.

<h3><u>2x + y = 5</u></h3>

Subtract 2x from both sides:

2x - 2x + y = - 2x + 5

y = -2x + 5 ⇒ This is the <u>slope-intercept form</u>, where the <u>slope</u>, <em>m</em> = -2, and the <u>y-intercept</u>, <em>b</em> = 5.

<h3><u /></h3><h3><u>3y = 9 − 6x </u></h3>

Divide both sides by 3 to isolate y:

3y = − 6x + 3

\frac{3y}{3} = \frac{-6x + 9}{3}

y = -2x + 3 ⇒ This is the <u>slope-intercept form</u>, where the <u>slope</u>, <em>m</em> = -2, and the <u>y-intercept</u>, <em>b</em> = 3.

<h2 /><h2>What do the equations have in common? </h2>

y = -2x + 5

y = -2x + 3

These equations have the same <u>slope</u>, m = -2.

<h2>How are they different?</h2>

They have different y-intercepts.

y = -2x + 5  ⇒ The <u>y-intercept</u> is (0, 5), where <em>b</em> = 5.

y = -2x + 3  ⇒ The <u>y-intercept</u> is (0, 3), where <em>b</em> = 3.

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