Respuesta :
The solution of the equations y=[tex]x^{2}[/tex]-x-22 and y=x-7 is that x=-3,5 and y=-10,-2.
Given equations y=[tex]x^{2} -x-22[/tex], y=x-7.
We are required to solve these equations for the value of x and y.
Equation is relationship between two or more variables expressed in equal to form.Equations of two variables look like ax+by=c.It may be a linear equation, quadratic equation and cubic equations.
The given equations are:
y=[tex]x^{2}[/tex]-x-22-----------1
y=x-7----------------2
Put the value of y from second equation in first equation.
x-7=[tex]x^{2}[/tex]-x-22
Solving
[tex]x^{2}[/tex]-x-x-22+7=0
[tex]x^{2}[/tex]-2x-15=0
[tex]x^{2}[/tex]-5x+3x-15=0
x(x-5)+3(x-5)=0
(x+3)(x-5)=0
x=-3,5
Put the values of x=-3 and 5 one by one to get the two values of y in second equation.
y=x-7
x=-3
y=-3-7
=-10
x=5
y=5-7
=-2
Values of y are -10 and -2.
Hence the values of x are-3 and 5 and values of y are -10,-2.
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