Question

What is the solution to the system of equations below? y = 1/4x + 2 and 3y = - 3/4x -6

no solution
infinitely many solutions
(–16, 6)
(–16, –2)

Answer 1

infinity many solutions

is the answer I did the exam

Answer 2

x = -8 and y= 0 → (-8, 0)

Explanation:

`\left\{\begin{array}{ccc}y=(1)/(4)x+2&(1)\\3y=-(3)/(4)x-6&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\3\left((1)/(4)x+2\right)=-(3)/(4)x-6\qquad\text{use the distributive property}\\\\(3)\left((1)/(4)x\right)+(3)(2)=-(3)/(4)x-6\\\\(3)/(4)x+6=-(3)/(4)x-6\qquad\text{subtract 6 from both sides}\\\\(3)/(4)x=-(3)/(4)x-12\qquad\text{add}\ (3)/(4)x\ \text{to both sides}\\\\(6)/(4)x=-12\qquad\text{multiply both sides by 4}\\\\6x=-48\qquad\text{divide both sides by 6}\\\\x=-8`

`\text{Put the value of x to (1):}\\\\y=(1)/(4)(-8)+2\\\\y=-2+2\\\\y=0`