Answered

IDNStudy.com, kung saan ang iyong mga tanong ay natutugunan ng mabilis na sagot. Ang aming komunidad ay handang magbigay ng malalim at maaasahang mga sagot, anuman ang kahirapan ng iyong mga katanungan.

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


Sagot :

KAntoineDoixidn

✒️ELIMINATION

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[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]

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[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

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

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

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

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

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

(ノ^_^)ノ

Salamat sa iyong presensya. Patuloy na magbahagi ng impormasyon at karanasan. Ang iyong kaalaman ay mahalaga sa ating komunidad. Salamat sa pagpili sa IDNStudy.com. Umaasa kami na makita ka ulit para sa mas maraming solusyon.