Respuesta :

Answer:  The required solution of the given system is

[tex](x,y)=(0,1),~(4,9).[/tex]

Step-by-step explanation:  We are given to solve the following system of equations by the method of substitution :

[tex]y=x^2-2x+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=2x+1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of y from equation (ii) in equation (i), we get

[tex]y=x^2-2x+1\\\\\Rightarrow 2x+1=x^2-2x+1\\\\\Rightarrow x^2-2x+1-2x-1=0\\\\\Rightarrow x^2-4x=0\\\\\Rightarrow x(x-4)=0\\\\\Rightarrow x=0,~x-4=0\\\\\Rightarrow x=0,4.[/tex]

When x = 0, then from equation (ii), we get

[tex]y=2\times0+1=0+1=1.[/tex]

When x = 4, then from equation (ii), we get

[tex]y=2\times4+1=8+1=9.[/tex]

Thus, the required solution of the given system is

[tex](x,y)=(0,1),~(4,9).[/tex]

facundo3141592

We want to solve the given system of equations by substitution.

The solution of the system is (0, 1).

We have the system:

y = x^2 + 2x + 1

y = 2x + 1

Solving by substitution means that we isolate one variable in one equation, and then substitute it on the other equation.

Here we can see that "y" is already isolated in the first equation, then we can replace that in the second one to get:

y = 2x + 1 = x^2 + 2x + 1

Then we have an equation only for x:

2x + 1 = x^2 + 2x + 1

Now we can solve the above equation:

0 = x^2 + 2x + 1 - 2x - 1

0 = x^2

0 = x

Now that we know the value of x, we can input it in one of the equations to find the value of y:

y = 2x + 1 = 2*0 + 1 = 1

y = 1

Then the solution is (0, 1).

If you want to learn more, you can read:

https://brainly.com/question/13997560

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