Question

What is the solution for the system of equations represented by: 4x-2y=12 and x=1/2 y + 3

Answer 1

The system of equations has infinitely many solutions in the form of:

`\left\{\begin{array}{ccc}y=2x-6\\y\in\mathbb{R}\end{array}\right`

Explanation:

`\left\{\begin{array}{ccc}4x-2y=12&(1)\\x=(1)/(2)y+3&(2)\end{array}\right\\\\\text{substitute}\ (2)\ \text{to}\ (1):\\\\4\left((1)/(2)y+3\right)-2y=12\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(4)\left((1)/(2)y\right)+(4)(3)-2y=12\\\\2y+12-2y=12\qquad\text{combine like terms}\\\\(2y-2y)+12=12\\\\12=12\qquad\bold{TRUE}`

`\text{solve for}\ y:\\\\4x-2y=12\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-2y=-4x+12\qquad\text{divide both sides by (-2)}\\\\y=2x-6`