Mathematics: Solve this system by substitution, 50 points! -x -y -z = -8 -4x +4y +5z = 7 2x+2z=4 Show steps please!

Solve this system by substitution, 50 points! - id508172023, anacecilianr2325

Ответ:

iBrain

04.02.2022

Mathematics

Solve:

-X - Y - Z =-8

- 4X +4Y +5Z=7

2X + 2Z =4 is the same as x + z = 2. Thus, z = 2 - x.

Subst. 2 - x for z in the 1st and second equations.

-X - Y - Z =-8 becomes -x - y - (2 -x) = -8

- 4X +4Y +5Z=7 becomes -4x + 4y + 5(2-x) = 7

Now we have 2 equations in only 2 unknowns. Let's simplify them!

-x - y - 2 + x = -8 which becomes -y = -6, or y = 6

-4x + 4y + 10 - 5x = 7 which becomes -9x + 4y = 7 - 10 = -3

Now substitute 6 for y in this last equation: -9x + 4(6) = -3, or

-9x + 24 = -3, or

-9x = - 27 => x = 3

Then x = 3, y = 6 and z = 2 - x, or z = 2-3, or z = -1.

The solution is (3, 6, -1). Check it!!

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Ответ:

cuppykittyy

09.05.2022

Mathematics

$a)\\2\times\frac{3}{4}=\frac{2}{1}\times\frac{3}{4}=\frac{1}{1}\times\frac{3}{4}=\frac{3}{2}=1\frac{1}{2}\\b)\\3\times\frac{3}{5}=\frac{3}{1}\times\frac{3}{5}=\frac{9}{5}=1\frac{4}{5}\\c)\\4\times\frac{1}{3}=\frac{4}{3}=1\frac{1}{3}\\d)\\6\times\frac{2}{5}=\frac{12}{5}=2\frac{2}{5}$
$e)\\\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}\\f)\\\frac{4}{5}\times\frac{2}{3}=\frac{8}{15}\\g)\\\frac{5}{6}\times\frac{3}{4}=\frac{5}{2}\times\frac{1}{4}=\frac{5}{8}\\h)\\\frac{1}{10}\times\frac{2}{3}=\frac{1}{5}\times\frac{1}{3}=\frac{1}{15}$
$i)\\2\frac{1}{5}\times\frac{1}{2}=\frac{2\times5+1}{5}\times\frac{1}{2}=\frac{11}{5}\times\frac{1}{2}=\frac{11}{10}=1\frac{1}{10}\\j)\\1\frac{1}{2}\times2\frac{1}{3}=\frac{1\times2+1}{2}\times\frac{2\times3+1}{3}=\frac{3}{2}\times\frac{7}{3}=\frac{1}{2}\times\frac{7}{1}=\frac{7}{2}=3\frac{1}{2}\\k)\\\frac{3}{4}\times2\frac{3}{4}=\frac{3}{4}\times\frac{2\times4+3}{4}=\frac{3}{4}\times\frac{11}{4}=\frac{33}{16}=2\frac{1}{16}$
$l)\\6\frac{2}{3}\times2\frac{1}{8}=\frac{6\times3+2}{3}\times\frac{2\times8+1}{8}=\frac{20}{3}\times\frac{17}{8}=\frac{5}{3}\times\frac{17}{2}=\frac{85}{6}=14\frac{1}{6}$

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Solve this system by substitution, 50 points! -x -y -z = -8

-4x +4y +5z = 7

2x+2z=4
Show steps please!

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