Question

Solve the system of equations using the substitution method.

y = -4x + 6
2x - y = 11

Answer 1

Answer:

By substituting the value of y from equation 1 in equation 2, we get,

2x - (-4x + 6) = 11

=> 2x + 4x -6 = 11

=> 6x = 11+6

=> 6x = 17

=> x = 17/6

Similarly substituting the resulted value of x in equation 1, we get the value of y as:

y = -4(17/6) + 6

=> y = -68/6 + 36/6

=> y = -32/6

=> y = -16/3

Answer 2

➲ We have two equations, solving them by using substitution method.

⠀⠀━━━━━━━━━━━━━━━━━━━━━

⠀

Equations

$\tt\longrightarrow{y = -4x + 6}$⠀⠀.... [1]

$\tt\longrightarrow{2x - y = 11}$⠀⠀.... [2]

⠀

Substituting the value of y in [2]

⠀

$\tt\longmapsto{2x - (-4x + 6) = 11}$

$\tt\longmapsto{2x + 4x - 6 = 11}$

$\tt\longmapsto{6x = 11 + 6}$

$\tt\longmapsto{6x = 17}$

$\tt\longmapsto{x = \dfrac{17}{6}}$

⠀

Now, putting the value of x in [1]

⠀

$\tt\longmapsto{y = -4 \times \dfrac{17}{6} + 6}$

⠀

$\tt\longmapsto{y = \dfrac{-34}{3} + 6}$

⠀

$\tt\longmapsto{y = \dfrac{-34 + 18}{3}}$

⠀

$\tt\longmapsto{y = \dfrac{-16}{3}}$

⠀

Hence,

$\tt\longrightarrow{x = \dfrac{17}{6}}$

$\tt\longrightarrow{y = \dfrac{-16}{3}}$