Chapter 11: Q. 40 (page 794)

In Problems 39–43, solve each system of equations.
$\{\begin{cases} 2 x y + y^{2} = 10 \\ 3 y^{2} - x y = 2 \end{cases}$

Short Answer

Expert verified

Solutions of the system of equations $\{\begin{cases} 2 x y + y^{2} = 10 \\ 3 y^{2} - x y = 2 \end{cases}$ are $(2 \sqrt{2}, \sqrt{2})$

Step by step solution

Step 1. Given data

The given system of equation is

$\{\begin{cases} 2 x y + y^{2} = 10 \\ 3 y^{2} - x y = 2 \end{cases}$

Step 2. Formation of the single-variable equation

Multiply 2 to both sides of the equation $3 y^{2} - x y = 2$

$2 (3 y^{2} - x y) = 2 (2) 6 y^{2} - 2 x y = 4$

so the new system of equation isrole="math" localid="1646947737732" $\{\begin{cases} 2 x y + y^{2} = 10 \\ 6 y^{2} - 2 x y = 4 \end{cases}$

add both equations of the system of equations,

$(2 x y + y^{2}) + (6 y^{2} - 2 x y) = 10 + 4 7 y^{2} = 14 y = \pm \sqrt{2}$

Step 4. Solution of the system of equations

Substitute $y = \sqrt{2}$ in equationrole="math" localid="1646947985401" $3 y^{2} - x y = 2$

$3 y^{2} - x y = 2 3 {(\sqrt{2})}^{2} - x \sqrt{2} = 2 x \sqrt{2} = 4 x = 2 \sqrt{2}$

Substitute $y = - \sqrt{2}$ in equation $3 y^{2} - x y = 2$

$3 y^{2} - x y = 2 3 {(- \sqrt{2})}^{2} - x (- \sqrt{2}) = 2 x \sqrt{2} = - 4 x = - 2 \sqrt{2}$

So solutions of the system of equations are $(2 \sqrt{2}, \sqrt{2}) & (- 2 \sqrt{2}, - \sqrt{2})$

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In Problems 39–43, solve each system of equations.
$\{\begin{cases} 2 x y + y^{2} = 10 \\ 3 y^{2} - x y = 2 \end{cases}$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Formation of the single-variable equation

Step 4. Solution of the system of equations

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In Problems 39–43, solve each system of equations.2xy+y2=103y2-xy=2

Short Answer

Step by step solution

Step 1. Given data

Step 2. Formation of the single-variable equation

Step 4. Solution of the system of equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Calculus

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 39–43, solve each system of equations.
$\{\begin{cases} 2 x y + y^{2} = 10 \\ 3 y^{2} - x y = 2 \end{cases}$