Solve by using substitution or elimination by addition2x - 5y = 273x + 2y = -7Select the correct choice below and fill in the answer box within your choice.A.The unique solution to the system is ___ ​(Type an ordered​ pair.)B.There are an infinite number of solutions.C.There is no solution.

Accepted Solution

Answer: A. The unique solution to the system is [tex](1,-5)[/tex]Step-by-step explanation:  You can follow these steps to solve the system of equations by the Elimination Method: - Multiply the first equation by -3 and the second equation by 2. - Add both equations and solve for "y". Then: [tex]\left \{ {{-3(2x - 5y) = -3(27)} \atop {2(3x + 2y)= 2(-7)}} \right.\\\\\left \{ {{-6x +15y = -81} \atop {6x + 4y= -14}} \right.\\..............................\\19y=-95\\y=-5[/tex] - Substitute the value of "y" into any original equation to find the value of "x". Then: [tex]2x - 5(-5) = 27\\\\2x=27-25\\\\2x=2\\\\x=1[/tex] Therefore, the unique solution to the system is [tex](1,-5)[/tex]