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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 11.70 (page 1140)

Solve the system by using substitution:
$\{\begin{cases} 4 x^{2} + y^{2} = 4 \\ y = x + 2 \end{cases}$

Short Answer

Expert verified

The solution is $(- \frac{4}{5}, \frac{6}{5}), (0, 2)$ .

Step by step solution

01

Step 1. Given Information

The given system is $\{\begin{cases} 4 x^{2} + y^{2} = 4 \\ y = x + 2 \end{cases}$ .

02

Step 2. Solve for x.

Substitute $y = x + 2$ into $4 x^{2} + y^{2} = 4$ and simplify.

$\begin{array}{rcl} 4 x^{2} + {(x + 2)}^{2} & = & 4 4 x^{2} + x^{2} + 4 + 4 x = 4 \\ 5 x^{2} + 4 x & = & 0 \\ x (5 x + 4) & = & 0 \\ x & = & 0, - \frac{4}{5} \end{array}$

03

Step 3. Solve for y.

Substitute $x = 0$ into $y = x + 2$ .

$\begin{array}{rcl} y & = & 0 + 2 \\ = & 2 \end{array}$

Substitute $x = - \frac{4}{5}$ into $y = x + 2$ .

$\begin{array}{rcl} y & = & - \frac{4}{5} + 2 \\ = & \frac{6}{5} \end{array}$

Thus, the solution set is $(- \frac{4}{5}, \frac{6}{5}), (0, 2)$ .

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