Respuesta :
Answer:
(- 2, 0 ) and (- 4, - 2 )
Step-by-step explanation:
Given the 2 equations
y = x + 2 → (1)
y = x² + 7x + 10 → (2)
Since both equations express y in terms of x we can equate them, that is
x² + 7x + 10 = x + 2 ( subtract x + 2 from both sides )
x² + 6x + 8 = 0 ← in standard form
(x + 2)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x + 4 = 0 ⇒ x = - 4
Substitute these values into (1) for corresponding values of y
x = - 2 : y = - 2 + 2 = 0 ⇒ (- 2, 0 )
x = - 4 : y = - 4 + 2 = - 2 ⇒ (- 4, - 2 )
Solutions are (- 2, 0 ) and (- 4, - 2 )
Solution of the system of equations are equals to [tex](-2,0)[/tex] and [tex](-4,-2)[/tex].
What is system of equations?
" System of equations is defined as the finite set of equation having common solution."
According to the question,
Given system of equations,
[tex]y= x+ 2[/tex] ______[tex](1)[/tex]
[tex]y = x^{2} +7x+10[/tex] ______[tex](2)[/tex]
Substitute the value of [tex]'y'[/tex] from system of equations [tex](1)[/tex] to [tex](2)[/tex] we get,
[tex]x^{2} + 7x + 10 = x+2\\\\\implies x^{2} + 7x-x+ 10-2=0\\\\\implies x^{2} + 6x+8 =0[/tex]
Factorize the equation to get the solution ,
[tex]x^{2} +6x+8=0\\\\\implies x^{2} +4x+2x+8=0\\\\\implies x(x+4) +2 (x+4)=0\\\\\implies (x+4)(x+2) =0\\\\\implies x +4 =0 or x +2 =0\\\\\implies x = -4 \ or\ x = -2[/tex]
When [tex]x= -2[/tex]
[tex]\implies y = -2+ 2\\\\\implies y =0[/tex]
When, [tex]x= -4[/tex]
[tex]\implies y = -4+2\\\\\implies y = -2[/tex]
Hence, solution of the system of equations are equals to [tex](-2,0)[/tex] and [tex](-4,-2)[/tex].
Learn more about system of equations here
brainly.com/question/12895249
#SPJ2
