Question

What is the x- value?

Answer 1

Answer:

x = 1

Step-by-step explanation:

$\bold{METHOD\ 1:}\\\\\text{Solve the system of equations:}\\\\\left\{\begin{array}{ccc}-4x-2y=-4&(1)\\y=-x+1&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\\\-4x-2(-x+1)=-4\qquad\text{use the distributive property}\\\\-4x+(-2)(-x)+(-2)(1)=-4\\\\-4x+2x-2=-4\qquad\text{add 2 to both sides}\\\\-4x+2x-2+2=-4+2\qquad\text{combine like terms}\\\\-2x=-2\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{-2}{-2}\\\\\boxed{x=1}$

$\bold{METHOD\ 2:}\\\\\text{Substitute each x value in the equations}\\\text{and check for the equality of the y value.}\\(1)\qquad-4x-2y=-4\qquad\text{add}\ 4x\ \text{to both sides}\\.\qquad-2y=4x-4\qquad\text{divide both sides by (-2)}\\.\qquad y=2x-2\\(2)\qquad y=-x+1\\\\\text{for}\ x=2:\\(1)\qquad y=2(2)-2=4-2=2\\(2)\qquad y=-2+1=-2\\different\ values\\\\\text{for}\ x=0:\\(1)\qquad y=2(0)-2=0-2=-2\\(2)\qquad y=-0+1=1\\different\ values$

$\text{for}\ x=1:\\(1)\qquad y=2(1)-2=2-2=0\\(2)\qquad y=-1+1=0\\the\ same\ values\\\\\text{for}\ x=-1:\\(1)\qquad y=2(-1)-2=-2-2=-4\\(2)\qquad y=-(-1)+1=1+1=2\\different\ values$

Answer 2

Answer: x = 1

Step-by-step explanation:

The system of equations is expressed as

- 4x - 2y = - 4- - - - - - - - - - - - - - - -1

y = - x + 1- - - - - - - - - - - - - - -2

We would apply the method of substitution by Substituting equation 2 into equation 1. It becomes

- 4x - 2(-x + 1) = - 4

- 4x +2x - 2 = - 4

- 2x - 2 = - 4

Adding 2 to the left hand side and the right hand side of the equation, it becomes

- 2x - 2 + 2 = - 4 + 2

- 2x = - 2

Dividing the left hand side and the right hand side of the equation by

- 2, it becomes

- 2x/- 2 = - 2/-2

x = 1

Substituting x = 1 into equation 2, it becomes

y = - 1 + 1

y = 0