Solve the System of Equations y=x^2-4x+6 y=x+2

$y = x^{2} - 4 x + 6$ $y = x + 2$

Eliminate the equal sides of each equation and combine.

$x^{2} - 4 x + 6 = x + 2$

Solve $x^{2} - 4 x + 6 = x + 2$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x^{2} - 4 x + 6 - x = 2$

Subtract $x$ from $- 4 x$ .

$x^{2} - 5 x + 6 = 2$

Subtract $2$ from both sides of the equation.

$x^{2} - 5 x + 6 - 2 = 0$

Subtract $2$ from $6$ .

$x^{2} - 5 x + 4 = 0$

Factor $x^{2} - 5 x + 4$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $4$ and whose sum is $- 5$ .

$- 4, - 1 + y = x + 2$

Write the factored form using these integers.

$(x - 4) (x - 1) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 4 = 0$

$x - 1 = 0 + y = x + 2$

Set $x - 4$ equal to $0$ and solve for $x$ .

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x - 1$ equal to $0$ and solve for $x$ .

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $(x - 4) (x - 1) = 0$ true.

$x = 4, 1$

Evaluate $y$ when $x = 4$ .

Substitute $4$ for $x$ .

$y = (4) + 2$

Substitute $4$ for $x$ in $y = (4) + 2$ and solve for $y$ .

Remove parentheses.

$y = 4 + 2$

Remove parentheses.

$y = (4) + 2$

Add $4$ and $2$ .

$y = 6$

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = (1) + 2$

Substitute $1$ for $x$ in $y = (1) + 2$ and solve for $y$ .

Remove parentheses.

$y = 1 + 2$

Remove parentheses.

$y = (1) + 2$

Add $1$ and $2$ .

$y = 3$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(4, 6)$

$(1, 3)$

The result can be shown in multiple forms.

Point Form:

$(4, 6), (1, 3)$

Equation Form:

$x = 4, y = 6$

$x = 1, y = 3$

Solve the System of Equations y=x^2-4x+6 y=x+2

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