Solve by Substitution x^2-y=0 , 7x+y=18

$x^{2} - y = 0$ , $7 x + y = 18$

Step 1

Subtract $7 x$ from both sides of the equation.

$y = 18 - 7 x$

$x^{2} - y = 0$

Step 2

Replace all occurrences of $y$ with $18 - 7 x$ in each equation.

Replace all occurrences of $y$ in $x^{2} - y = 0$ with $18 - 7 x$ .

$x^{2} - (18 - 7 x) = 0$

$y = 18 - 7 x$

Simplify the left side.

Simplify each term.

Apply the distributive property.

$x^{2} - 1 \cdot 18 - (- 7 x) = 0$

$y = 18 - 7 x$

Multiply $- 1$ by $18$ .

$x^{2} - 18 - (- 7 x) = 0$

$y = 18 - 7 x$

Multiply $- 7$ by $- 1$ .

$x^{2} - 18 + 7 x = 0$

$y = 18 - 7 x$

$x^{2} - 18 + 7 x = 0$

$y = 18 - 7 x$

$x^{2} - 18 + 7 x = 0$

$y = 18 - 7 x$

$x^{2} - 18 + 7 x = 0$

$y = 18 - 7 x$

Step 3

Solve for $x$ in $x^{2} - 18 + 7 x = 0$ .

Factor $x^{2} - 18 + 7 x$ 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 $- 18$ and whose sum is $7$ .

$- 2, 9$

$y = 18 - 7 x$

Write the factored form using these integers.

$(x - 2) (x + 9) = 0$

$y = 18 - 7 x$

$(x - 2) (x + 9) = 0$

$y = 18 - 7 x$

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

$x - 2 = 0$

$x + 9 = 0$

$y = 18 - 7 x$

Set $x - 2$ equal to $0$ and solve for $x$ .

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

$y = 18 - 7 x$

Add $2$ to both sides of the equation.

$x = 2$

$y = 18 - 7 x$

$x = 2$

$y = 18 - 7 x$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

$y = 18 - 7 x$

Subtract $9$ from both sides of the equation.

$x = - 9$

$y = 18 - 7 x$

$x = - 9$

$y = 18 - 7 x$

The final solution is all the values that make $(x - 2) (x + 9) = 0$ true.

$x = 2, - 9$

$y = 18 - 7 x$

$x = 2, - 9$

$y = 18 - 7 x$

Step 4

Replace all occurrences of $x$ with $2$ in each equation.

Replace all occurrences of $x$ in $y = 18 - 7 x$ with $2$ .

$y = 18 - 7 \cdot 2$

$x = 2$

Simplify the right side.

Simplify $18 - 7 \cdot 2$ .

Multiply $- 7$ by $2$ .

$y = 18 - 14$

$x = 2$

Subtract $14$ from $18$ .

$y = 4$

$x = 2$

$y = 4$

$x = 2$

$y = 4$

$x = 2$

$y = 4$

$x = 2$

Step 5

Replace all occurrences of $x$ with $- 9$ in each equation.

Replace all occurrences of $x$ in $y = 18 - 7 x$ with $- 9$ .

$y = 18 - 7 \cdot - 9$

$x = - 9$

Simplify the right side.

Simplify $18 - 7 \cdot - 9$ .

Multiply $- 7$ by $- 9$ .

$y = 18 + 63$

$x = - 9$

Add $18$ and $63$ .

$y = 81$

$x = - 9$

$y = 81$

$x = - 9$

$y = 81$

$x = - 9$

$y = 81$

$x = - 9$

Step 6

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

$(2, 4)$

$(- 9, 81)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, 4), (- 9, 81)$

Equation Form:

$x = 2, y = 4$

$x = - 9, y = 81$

Step 8

Solve by Substitution x^2-y=0 , 7x+y=18

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