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12 votes
12 votes
{x + y = 2

{y = -1/4 x^2+3

1. In two or more complete sentences, explain how to solve the system of equations algebraically.

2. Solve the system of equations. In your final answer, include all of your work.

{x + y = 2 {y = -1/4 x^2+3 1. In two or more complete sentences, explain how to solve-example-1
User Wislon
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2 Answers

18 votes
18 votes

1) I put them in two separate brakets.

2) I solved it by equating both of them.

{x + y = 2 {y = -1/4 x^2+3 1. In two or more complete sentences, explain how to solve-example-1
User Giacomo M
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8 votes
8 votes

Answer:

1. Substitute for y in the first equation. Solve for x by completing the square. Substitute for x in the first equation to find y.

2. (x, y) = (2+2√2, -2√2) and (2-2√2, 2√2)

Explanation:

1.

The first equation is a linear equation in standard form. The second equation is a quadratic equation giving an expression for y. The system can be solved by using the second equation to substitute for y in the first equation. After the resulting equation is put in suitable form, the irrational solutions can be found by completing the square. Then the y-values can be found by substituting the x-values into either of the given equations. Usually, it is easiest to substitute into the linear equation.

__

2.

Substituting for y in the first equation:

x +(-1/4x^2 +3) = 2

Multiplying by -4 to eliminate the fraction and make the leading coefficient 1, we have ...

-4x +x^2 -12 = -8

x^2 -4x = 4 . . . . . . add 12

x^2 -4x +4 = 8 . . . . add 4 to complete the square

(x -2)^2 = 8 . . . . . . write as a square

x -2 = ±√8 = ±2√2 . . . . take the square root

x = 2 ±2√2 . . . . . . add 2

Solving the first equation for y, we get ...

y = 2 -x

Substituting the values of x we found gives ...

y = 2 -(2 ±2√2) = ∓2√2

Solutions are ...

(x, y) = (2+2√2, -2√2) and (2-2√2, 2√2)

User Oscerd
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