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Directions: convert each linear equation in two variables to slope - intercept form. Show your solution


1. 3(x - 2) + 4 (y + 1) = 5x - y + 10



2. 6x - 2 (y + 3) = 2 (x + 5) - 12​

Sagot :

Answer:

CONVERTING LINEAR EQUATION INTO STANDARD FORM

Solution:

1. [tex]\sf{3 (x - 2) + 4 (y + 1) = 5x - y + 10}[/tex]

  • Distributive Property

[tex]\sf{3 (x) + 3 (-2) + 4 (y) + 4(1) = 5x - y + 10}[/tex]

[tex]\sf{3x - 6 + 4y + 4 = 5x - y + 10}[/tex]

  • Reorder and combine the similar terms.

[tex]\sf{3x + 4y - 6 + 4 = 5x - y + 10}[/tex]

[tex]\sf{3x + 4y - 2 = 5x - y + 10}[/tex]

  • Transposition Method

[tex]\sf{3x + 4y + y = 5x + 10 + 2}[/tex]

[tex]\sf{3x + 5y = 5x + 12}[/tex]

  • Combine similar terms

[tex]\sf{3x - 3x + 5y = 5x - 3x + 12}[/tex]

[tex]\sf{5y = 2x + 12}[/tex]

  • Divide both sides by 5.

[tex]\sf{\frac{5y}{5} = \frac{2x + 12}{5}}[/tex]

[tex]\sf{y = \frac{2}{5}x + \frac{12}{5}}[/tex]

Final answer

[tex]\boxed{\sf{y = \frac{2}{5}x + \frac{12}{5}}}[/tex]

2. [tex]\sf{6x - 2 (y + 3) = 2 (x + 5) - 12}[/tex]

  • Simplify.

[tex]\sf{6x - 2y + 6 = 2x + 10 - 12}[/tex]

[tex]\sf{6x - 2y + 6 = 2x - 2}[/tex]

  • Transpose the constant and 6x to the right side.

[tex]\sf{-2y = 2x - 6x - 6 - 2}[/tex]

  • Simplify.

[tex]\sf{-2y = -4x - 8}[/tex]

  • Divide both sides by -2.

[tex]\sf{\frac{-2y}{-2} = \frac{-4x - 8}{-2}}[/tex]

[tex]\boxed{\sf{y = 2x + 4}}[/tex]

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