Question

What is the solution to the system of equations?

Answer 1

`\large\boxed{\left(7,\ (13)/(3)\right)}`

Explanation:

You must use the algebraic method: substitution or elimination.

I will solve a given system of equations the substitution method.

`\left\{\begin{array}{ccc}y=(1)/(3)x+2&(1)\\\\y=(4)/(3)x-5&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\(4)/(3)x-5=(1)/(3)x+2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot(4)/(3\!\!\!\!\diagup_1)x-(3)(5)=3\!\!\!\!\diagup^1\cdot(1)/(3\!\!\!\!\diagup_1)x+(3)(2)\\\\4x-15=x+6\qquad\text{add 15 to both sides}\\\\4x=x+21\qquad\text{subtract x from both sides}\\\\3x=21\qquad\text{divide both sides by 3}\\\\x=7\\\\\text{put the value of x to the first equation}\\\\y=(1)/(3)\cdot7+2\\\\y=(7)/(3)+(6)/(3)\\\\y=(13)/(3)`