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Serga [27]
3 years ago
10

Can someone help me with this substitution method for algebra Y=4*-3x 5x-y=22

Mathematics
1 answer:
alexira [117]3 years ago
7 0
y=4-3x\\
5x-y=22\\\\
5x-(4-3x)=22\\
5x-4+3x=22\\
8x=26\\
x=\dfrac{26}{8}=\dfrac{13}{4}\\\\
y=4-3\cdot\dfrac{13}{4}\\
y=4-\dfrac{39}{4}\\
y=\dfrac{16}{4}-\dfrac{39}{4}\\
y=-\dfrac{23}{4}\\\\
\boxed{(x,y)=\left(\dfrac{13}{4},-\dfrac{23}{4}\right)}
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Step-by-step explanation:

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Dividing 0.3 both side

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Gekata [30.6K]

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y=\displaystyle-\frac{4}{3}x+22

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept
  • Parallel lines always have the same slope (<em>m</em>)

<u>Determine the slope (</u><em><u>m</u></em><u>):</u>

<u />y=\displaystyle-\frac{4}{3}x -1<u />

The slope of the given line is \displaystyle-\frac{4}{3}, since it is in the place of <em>m</em> in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be \displaystyle-\frac{4}{3}. Plug this into y=mx+b:

y=\displaystyle-\frac{4}{3}x+b

<u>Determine the y-intercept (</u><em><u>b</u></em><u>):</u>

y=\displaystyle-\frac{4}{3}x+b

To find the y-intercept, plug in the given point (6,14) and solve for <em>b</em>:

14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22

Therefore, the y-intercept of the line is 22. Plug this back into y=\displaystyle-\frac{4}{3}x+b:

y=\displaystyle-\frac{4}{3}x+22

I hope this helps!

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