Solve the system of linear equations using the substitution method. Y = 6x + 11 and 2y - 4x = 14 A. (-1, 5) B. (-4, 3) C. (-2, 2) D. (-4, 4)

Question

asked Apr 18, 2023 221k views

2 Answers

Kalisjoshua · Answer 1 · 2023-04-24T16:25:41+0000

Option A. (-1,5)

${ \blue{ \tt{x = - 1}}}$

${ \blue{ \tt{y = 5}}}$

Explanation:

${ \bold{ \orange{y = 6x + 11}}} \: → \: { \bold{ \green{ {eq}^(n)(1)}}}$

${ \bold{ \orange{2y - 4x = 14}}} \: →{ \green{ \bold{ {eq}^(n)(2)}}}$

Substitute the value of y in Equation no. (2) then,

${ \bold{ \orange{2(6x + 11) - 4x = 14}}}$

${ \bold{ \orange{12x + 22 - 4x = 14}}}$

${ \bold{ \orange{8x + 22 = 14}}}$

${ \bold{ \orange{8x = 14 - 22}}}$

${ \bold{ \orange{8x = - 8}}}$

${ \bold{ \orange{x = ( - 8)/( \: \: \: 8)}}}$

${ \bold{ \orange{x = - 1}}}$

Substitute the value of x in Equation no. (1) then,

${ \bold{ \orange{y = 6x + 11}}}$

${ \bold{ \orange{y = 6(-1) + 11}}}$

${ \bold{ \orange{y = -6 + 11}}}$

${ \bold{ \orange{y = 5}}}$