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Vaselesa [24]
3 years ago
5

Determine the solution using substitution y=3/2x-6 2y=7-4x

Mathematics
2 answers:
Vika [28.1K]3 years ago
6 0

Answer:

x = 19/7 , y= -27/14

Step-by-step explanation:

ira [324]3 years ago
4 0
(19/7, -27/14) x= 19/7 y=-27/14
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Solve each equation by using the square roots property round to the nearest hundredth if necessary
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A given line has the equation 10x + 2y = −2.
worty [1.4K]

The equation is \boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }

<h3>Further explanation </h3>

This case asking the end result in the form of a slope-intercept.

<u>Step-1: find out the gradient. </u>

10x + 2y = -2

We isolate the y variable on the left side. Subtract both sides by 10x, we get:

2y = - 10x - 2  

Divide both sides by two

y = -5x -1

The slope-intercept form is \boxed{ \ y = mx + c \ }, with the coefficient m as a gradient. Therefore, the gradient is m = -5.

If you want a shortcut to find a gradient from the standard form, implement this:  

\boxed{ \ ax + by = k \rightarrow m = - \frac{a}{b} \ }

10x + 2y = −2 ⇒ a = 10, b = 2

\boxed{m = - \frac{10}{2} \rightarrow m = -5}

<u>Step-2:</u> the conditions of the two parallel lines

The gradient of parallel lines is the same \boxed{ \ m_1 = m_2 \ }. So \boxed{m_1 = m_2 = -5}.

<u>Final step:</u> figure out the equation, in slope-intercept form, of the parallel line to the given line and passes through the point (0, 12)

We use the point-slope form.

\boxed{ \ \boxed{ \ y - y_1 = m(x - x_1)} \ }

Given that

  • m = -5
  • (x₁, y₁) = (0, 12)  

y - 12 = - 5(x - 0)

y - 12 = - 5x

After adding both sides by 12, the results is \boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }

<u>Alternative steps </u>

Substitutes m = -5 and (0, 12) to slope-intercept form \boxed{ \ y = mx + c \ }

12 = -5(0) + c

Constant c is 12 then arrange the slope-intercept form.

Similar results as above, i.e. \boxed{ \ y = - 5x + 12 \ or \ y = 12 - 5x} \ }

<u>Note: </u>

\boxed{Standard \ form: ax + by = c, with \ a > 0}

\boxed{Point-slope \ form: y - y_1 = m(x - x_1)}

\boxed{Slope-intercept \ form: y = mx + k}

<h3>Learn more </h3>
  1. A similar problem brainly.com/question/10704388
  2. Investigate the relationship between two lines brainly.com/question/3238013
  3. Write the line equation from the graph brainly.com/question/2564656

Keywords: given line, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, through the point, constant

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3 years ago
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