Answer:
(2, 7) or (-6, 1)
Step-by-step explanation:
We are given two equations:
[tex]y=x+5[/tex]; and
[tex]y = x^2+5x-7[/tex]
Since y is the subject for both the equations so we can put the values of y equal to each other to get:
[tex]x+5=x^2+5x-7[/tex]
[tex]x^2+5x-x-7-5=0[/tex]
[tex]x^2+4x-12=0[/tex]
Factorizing the expression to get:
[tex]x^2-2x+6x-12=0[/tex]
[tex]x(x-2)+6(x-2)=0[/tex]
[tex](x-2) (x+6) = 0[/tex]
[tex]x=2, x= -6[/tex]
Putting x = 2 and x = -6 in any of the equations to get the values of y:
[tex]y=x+5[/tex]
[tex]y =2+5[/tex]
[tex]y=7[/tex]
and
[tex]y =(-6)+5[/tex]
[tex]y=1[/tex]
Therefore, solution to these equation is (2, 7) or (-6, 1).
