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fiasKO [112]
3 years ago
15

Find the coordinates of the points of intersection of the graphs without building them: 5x–4y=16 and x–2y=6

Mathematics
1 answer:
Genrish500 [490]3 years ago
3 0

\bf \begin{cases} 5x-4y=16\\ \cline{1-1} x-2y=6\\ \boxed{x}=6+2y \end{cases}~\hspace{7em}\stackrel{\textit{substituting \underline{x} in the first equation}}{5\left( \boxed{6+2y} \right)-4y=16} \\\\\\ 30+10y-4y=16\implies 30+6y=16\implies 6y=-14 \\\\\\ y=-\cfrac{14}{6}\implies y=-\cfrac{7}{3}\implies \blacktriangleright y=-2\frac{1}{3} \blacktriangleleft \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{since we know that}}{x=6+2y}\implies x=6+2\left( -\cfrac{7}{3} \right)\implies x=6+\left(-\cfrac{14}{3} \right) \\\\\\ x=6-\cfrac{14}{3}\implies x=\cfrac{18-14}{3}\implies x=\cfrac{4}{3}\implies \blacktriangleright x=1\frac{1}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 1\frac{1}{3} ~,~-2\frac{1}{3}\right)~\hfill

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A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution. How many of each should be used ?
schepotkina [342]

Answer:

The number of liters of 25% acid solution = x = 160 liters

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Step-by-step explanation:

Let us represent:

The number of liters of 25% acid solution = x

The number of liters of 40% acid solution = y

Our system of Equations =

x + y = 240 liters....... Equation 1

x = 240 - y

A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution.

25% × x + 40% × y = 240 liters × 30%

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We substitute 240 - y for x in Equation 2

0.25(240 - y)+ 0.4y = 72

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Collect like terms

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x = 240 liters - 80 Liters

x = 160 liters

Therefore,

The number of liters of 25% acid solution = x = 160 liters

The number of liters of 40% acid solution = y = 80 liters

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