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nika2105 [10]
3 years ago
12

Solve each system by substitution x+12y=68

Mathematics
2 answers:
Korvikt [17]3 years ago
7 0
\large\begin{array}{l} \textsf{Solve the system by substitution:}\\\\ \left\{\! \begin{array}{rrrrrc} \mathsf{x}&\!\!\!+\!\!\!&\mathsf{12y}&\!\!\!=\!\!\!&\mathsf{68}&\quad\mathsf{(i)}\\ \mathsf{x}&\!\!\!=\!\!\!&\mathsf{8y}&\!\!\!-\!\!\!&\mathsf{12}&\quad\mathsf{(ii)} \end{array} \right. \end{array}


\large\begin{array}{l} \textsf{Substitute x from (ii) into (i):}\\\\ \mathsf{(8y-12)+12y=68}\\\\ \mathsf{8y+12y=68+12}\\\\ \mathsf{20y=80}\\\\ \mathsf{y=\dfrac{80}{20}}\\\\ \boxed{\begin{array}{c}\mathsf{y=4} \end{array}} \end{array}


\large\begin{array}{l} \textsf{Substitute y back into (ii):}\\\\ \mathsf{x=8\cdot 4-12}\\\\ \mathsf{x=32-12}\\\\ \mathsf{x=20}\\\\ \boxed{\begin{array}{c} \mathsf{x=20} \end{array}}\\\\\\ \textsf{Solution: }\mathsf{S={\{(20;\,4)\}}} \end{array}


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ololo11 [35]3 years ago
4 0
Substitute x=8y-12 into first equation
8y-12+12y=68
20y=68+12
20y=80
y=80/20
y=4

substitute y=4 in 2nd equ
x=8(4)-12
x=32-12
x=20
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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

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<em />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Rewrite:                                                                                                             \displaystyle 3^{6x + 18} < 3^{3(3x)}
  2. Set:                                                                                                                     \displaystyle 6x + 18 < 3(3x)
  3. Factor:                                                                                                               \displaystyle 3(2x + 6) < 3(3x)
  4. [Division Property of Equality] Divide 3 on both sides:                                  \displaystyle 2x + 6 < 3x
  5. [Subtraction Property of Equality] Subtract 3x on both sides:                       \displaystyle -x + 6 < 0
  6. [Subtraction Property of Equality] Subtract 6 on both sides:                        \displaystyle -x < -6
  7. [Division Property of Equality] Divide -1 on both sides:                                 \displaystyle x > 6
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