Question

Y=-x+5 x-y=-9 how many solutions are there show work

Answer 1

Answer:

This system of equations will have only one solution.

Step-by-step explanation:

Given,

Algebraic equation given are

                                                    $Y=-x+5\\ \\ x+y-5=0----(1)\\ \\ x-y=-9\\ \\ x-y+9=0----(2)$

Comparing equation (1) and (2) with equation,

                     

                           $a_1x + b_1y + c_1 = 0\\ \\ a_2x + b_2y + c_2 = 0$

Where $a_1, b_1, c_1, a_2, b_2, c_2$ are all real numbers.

Comparing the coefficients,

                 $\frac{a_1}{a_2} =\frac{1}{1}=1\\ \\ \frac{b_1}{b_2}=\frac{1}{-1} =-1\\ \\ \frac{c_1}{c_2}=\frac{-5}{9}$

                                $\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$

       Hence, this system of equations will have only one solution.