Question

Use substitution to determine the solution of the system of equations.y = −2x − 72y − x = 1A.(−1,0)B.(21/2,−28)C.(−6,−5/2)D.(−3,−1)

Answer 1

Given equations are

`y=-2x-7`
`2y-x=1`
`\text{ Substitute y=-2x-7 in equation 2y-x=1 as follows.}`

`2(-2x-7)-x=1`

Multiplying 2 and (-2x-7), we get

`2(-2x)-2*7-x=1`

`-4x-14-x=1`

`-5x-14=1`

Adding 14 on both sides, we get

`-5x-14+14=1+14`

`-5x=15`

Multiplying both sides by (-5), we get

`-(5x)/(-5)=(15)/(-5)`

`x=-3`

`\text{ Substitute x=-3 in the equation y=-2x-7 as follows.}`
`y=-2(-3)-7`

`y=6-7`
`y=-1`

Hence we get (x, y)= ( -3, -1).

Option D) is correct.