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stepan [7]
3 years ago
10

X + 5y = 24 5x = 12 - y

Mathematics
1 answer:
Travka [436]3 years ago
8 0

Answer: x = 3/2 y = 9/2

Step-by-step explanation:

Subtract  

5 y

Replace all occurrences of x

from both sides of the equation.

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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4
Dmitry [639]

Answer:

  • \boxed{\sf Standard-form :x + 4y -17=0 }\\

  • \boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

\longrightarrow x + 4y = 7\\

Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;

\longrightarrow 4y = -x + 7  \\

\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\

On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,

\longrightarrow m =\dfrac{-1}{4}\\

\longrightarrow c =\dfrac{7}{4}\\

Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,

\longrightarrow m_{||)}=\dfrac{-1}{4}\\

Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,

\longrightarrow y - y_1 = m(x-x_1) \\

On substituting the respective values ,

\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\

\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\

\longrightarrow 4(y -5 ) =-1(x +3) \\

\longrightarrow 4y -20 = - x -3 \\

\longrightarrow x + 4y -20+3=0\\

\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\

Again the equation can be rewritten as ,

\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5  \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4}  \\

\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{  y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\

6 0
2 years ago
PLZ HELP ME ITS DUE TOMORROW!!!!
Veronika [31]

Anywhere from 7 - 13 hours

8 0
2 years ago
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Write the equation of the line that passes through (3, –2) and has a slope of 4 in point-slope form.
Likurg_2 [28]
A. would be y=4x-14
B. would be y=4x+11
C. would be y=x/4 - 11/4
D. would be y=x/4 + 7/2
Hope this helps! :)
4 0
3 years ago
your family gives you $3 on the first day, $3.50 on the second, $4 on the third, and so on, increasing by 50 cents per day. In a
never [62]
325.5 if I did my math right
4 0
2 years ago
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3=c/5+2... how do I solve for c??
expeople1 [14]
Primeiro Você IRA Dividir o c (APENAS Colocar 5 + 2 embaixo do c). Depois faça a soma 5 + 2 = 7. Então faça o mmc (mínimo múltiplo comum) entre 7 e 1(o 1 é invisível, mas continua estando embaixo do 3). Deu 7 o mmc. Transforme seus números em frações, com o denominador 7. Transforme os números em frações o 3 virá 21, pois você divide em baixo e multiplica em baixo, e o c continua normal, pois já estava em baixo de 7. Como é para descobrir uma incógnita você tira os denominadores e ficará 21 = c.

3 = c/5 + 2
3 = c/7
21/7 = c/7
21 = c
4 0
2 years ago
Read 2 more answers
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