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

$2(-2x)-2\times7-x=1$

$-4x-14-x=1$

$-5x-14=1$

Adding 14 on both sides, we get

$-5x-14+14=1+14$

$-5x=15$

Multiplying both sides by (-5), we get

$-\frac{5x}{-5}=\frac{15}{-5}$

$x=-3$

$\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.