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sleet_krkn [62]

3 years ago

9

how many solutions does a system of two linear equations have if the slope of each equation is different and the y-intercepts ar

e the same?

1 answer:

omeli [17]3 years ago

8 0

The system would have one solution and it would be where the equations intersect at the y-intercept.

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2 years ago

Read 2 more answers

3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Find the equation of the line passing through (4, 5) and parallel to </em>

<em> 3x-2y=4.</em>

<em />

<em> </em> $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

$\rule{300}{3}$

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

$\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}$

$\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}$

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2 years ago

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san4es73 [151]

Answer:

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Step-by-step explanation 3

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3 years ago

Marcus is planning a budget. He plans to spend less than 25% of his allowance each week on entertainment. Last week Marcus spent

g100num [7]

Marcus went above his budget as 25% percent of his allowance would be $5, and he went $2.42 over.

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3 years ago

The value of y varies directly with x. When y=4, x=12. What is the value of y when x is 42

Anna35 [415]

Answer:

y would be 14

Step-by-step explanation:

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3 years ago