Question

What is the solution to the following system of equations? y = x^(2) + 10x + 11 y = x^(2) + x - 7

Answer 1

`\sf\\\textsf{Given:}\\y=x^2+10x+11............(1)\\y=x^2+x-7...........(2)\\\\\textsf{Equating equations(1) and (2),}\\x^2+10x+11=x^2+x-7\\\textsf{or, }10x+11=x-7\\\textsf{or, }10x-x=-11-7\\\textsf{or, }9x=-18\\\textsf{or, }x=-2`

`\sf\\\textsf{Put x = }-2\textsf{ in equation (2),}\\y=(-2)^2+(-2)-7=4-2-7=-5`

`\sf\\\therefore\ x=-2\ and\ y=-5`