Question

How do you solve `2x+y= -1` and `-x+y= -7` using substitution?

Answer 1

`color(magenta)(x = 2, y = -5`

Explanation:

`2x + y = -1 " Eqn (1)"`

`-x + y = -7`

`x - y = 7 " Eqn (2)"`

`color(crimson)("1. Using elimination process"`

Adding Eqns (1) & (2),

`2x + x +cancel( y - y) = -1 + 7`

`3x = 6 " or " x = 2`

Substituting value of 'x' in Eqn (1),

`2*2 + y = -1`

`y = -1 + -4 = -5`

`color(crimson)("2. Using substitution process"`

`x = y + 7 " from Eqn (2)"`

Substituting value of 'x' in Eqn (1)",

`2 * (y + 7) + y = -1`

`3y = -1 -14 = -15`

`y = -5`

Substituting value of 'y ' in Eqn (2),

`x - (-5) = 7`

`x = 7 - 5 = 2`