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3 years ago

How to substitute 3x+3y=-3 and y=5x-1?

1 answer:

7 0

Since y = 5x-1, we can fill it into 3x + 3y = -3. First, let's look at relating to a simpler equation. Let's say that x + y = 9 and y = 3 + 5. Now, we can fill it in to get that x + (3 + 5) = 9. Now, we know that 3+5 is 8, so x + 8 = 9. Now, x = 1. Likewise, we can do the same. For 3x + 3y = -3, all we need to do is to switch the y in 3x + 3y = -3 with 5x - 1. So it would become 3x + 3(5x - 1) = -3. Now we distribute to get 3x + 15x - 3 = -3. Now add three to both sides to get 3x + 15x = 0. Now simplify to get 18x = 0. Now we know that x = 0. Now fill x into y = 5x - 1. So y = 5(0) - 1. Now we know that y = -1.

To check fill in the answer to 3x + 3y = -3.
3(0) + 3(-1) = -3
0 + (-3) = -3
0 - 3 = -3
-3 = -3
Now that our check is completed we now know that x is 0 and y is -1.

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Graphing $y=- \frac{2}{3}x+490$ using slope-intercept method:
a) The slope is a negative slope. The line will go 'down hill'
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c) The line will intercept the x-axis at y = 0
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So, x-intercept is at (735, 0)

The graph of this function is shown below. The intercepts are labelled at:
y = 490
x = 735

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Next month's profit equation

$2x+3y=1593$

Rewriting this into slope-equation form

$3y = -2x+1593$
$y=- \frac{2}{3}+ \frac{1593}{3}$
$y= - \frac{2}{3}+531$

The gradient, $m$ , equals to $- \frac{2}{3}$
The y-intercept, $c$ , equals to 531

The equation still has the same gradient with last month's profit equation but different y-intercept.

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A linear graph show points of (0, 300) and (450, 0)

We work out the slope:
$\frac{300-0}{0-450} = \frac{300}{-450}=- \frac{20}{30} =- \frac{2}{3}$

Y-intercept at x = 0, so it's at y = 300

Equation $y = - \frac{2}{3}+300$

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