Answered

Solve each System of Linear Equations by using Elimination Method
1. 4x – y = 14 x + y = 11 2. 4x – y = 9 3x + 2y = 4 3. x + y = 10 x – y = 2


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KAntoineDoixviz

✒️ELIMINATION

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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \:\: \rm 1) \; x = 5 \;,\; y = 6 [/tex]

[tex] \qquad \Large \:\: \rm 2) \; x = 2 \;,\; y = \text-1 [/tex]

[tex] \qquad \Large \:\: \rm 3) \; x = 6 \;,\; y = 4 [/tex]

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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

Number 1:

Give the two equations.

  • [tex] \begin{cases} 4x - y = 14 \\ x + y = 11 \end{cases} \quad \begin{align} \tt{(eq. \: 1)} \\ \tt{(eq. \: 2)} \end{align} [/tex]

Eliminate y to find x by adding the two equations.

  • [tex] 4x - \cancel y + x + \cancel y = 14 + 11 [/tex]

  • [tex] 4x + x = 14 + 11 [/tex]

  • [tex] 5x = 25 [/tex]

  • [tex] \frac{5x}5 = \frac{25}5 \\ [/tex]

  • [tex] x = 5 [/tex]

Thus, the value of x is 5. Substitute it to either one of the equation to find y.

  • [tex] x + y = 11 \:;\: x = 5 [/tex]

  • [tex] 5 + y = 11 [/tex]

  • [tex] y = 11 - 5 [/tex]

  • [tex] y = 6 [/tex]

Therefore, the value of y is 6

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Number 2:

Give the two equations.

  • [tex] \begin{cases} 4x - y = 9 \\ 3x + 2y = 4 \end{cases} \quad \begin{align} \tt{(eq. \: 1)} \\ \tt{(eq. \: 2)} \end{align} [/tex]

Multiply the first equation by 2 to match the opposite coefficients of y.

  • [tex] 2(4x - y) = 2(9) [/tex]

  • [tex] 8x - 2y = 18 [/tex]

Eliminate y to find x by adding the two equations.

  • [tex] 8x - \cancel {2y} + 3x + \cancel {2y} = 18 + 4 [/tex]

  • [tex] 8x + 3x = 18 + 4 [/tex]

  • [tex] 11x = 22 [/tex]

  • [tex] \frac{11x}{11} = \frac{\,22\,}{11} \\ [/tex]

  • [tex] x = 2 [/tex]

Thus, the value of x is 2. Substitute it to either one of the equation to find y.

  • [tex] 4x - y = 9 \:;\: x = 2 [/tex]

  • [tex] 4(2) - y = 9 [/tex]

  • [tex] 8 - y = 9 [/tex]

  • [tex] \text-y = 9 - 8 [/tex]

  • [tex] \text- y = 1 [/tex]

  • [tex] y = \text-1 [/tex]

Therefore, the value of y is -1

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Number 3:

Give the two equations.

[tex] \begin{cases} x + y = 10 \\ x - y = 2 \end{cases} \quad \begin{align} \tt{(eq. \: 1)} \\ \tt{(eq. \: 2)} \end{align} [/tex]

Eliminate y to find x by adding the two equations.

  • [tex] x - \cancel y + x + \cancel y = 10 + 2 [/tex]

  • [tex] x + x = 10 + 2 [/tex]

  • [tex] 2x = 12 [/tex]

  • [tex] \frac{2x}2 = \frac{12}2 \\ [/tex]

  • [tex] x = 6 [/tex]

Thus, the value of x is 6. Substitute it to either one of the equation to find y.

  • [tex] x + y = 10 \:;\: x = 6 [/tex]

  • [tex] 6 + y = 10 [/tex]

  • [tex] y = 10 - 6 [/tex]

  • [tex] y = 4 [/tex]

Therefore, the value of y is 4

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