Mathematics: 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)

What is the solution to the system of equations below?

Ответ:

AmityHeart

10.03.2022

x = -8 and y= 0 → (-8, 0)

Step-by-step explanation:

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