Question

How many solutions does the following system of equations have

Answer 1

D. Zero

Explanation:

`\left\{\begin{array}{ccc}y=(5)/(2)x+2&(1)\\2y=5x+8&(2)\end{array}\right\\\\\text{substitute (1) to (2)}:\\\\2\left((5)/(2)x+2\right)=5x+8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(2)\left((5)/(2)x\right)+(2)(2)=5x+8\\\\5x+4=5x+8\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\4=8\qquad\bold{FALSE}\\\\\text{The system of equations has no solution.}`