Chapter 11: Q. 75 (page 757)

Algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x + 3 y = 11 \\ 5 x + 7 y = 24 \end{cases}$

Short Answer

Expert verified

The values of x and y are $- 5 & 7$

Step by step solution

Step 1.Given information

Given equation are $2 x + 3 y = 11 & 5 x + 7 y = 24$

Step 2.Conversion of equations

Matrix form $[\begin{matrix} 2 & 3 \\ 5 & 7 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 11 \\ 24 \end{matrix}]$

Step 3.Reduction of matrix

Reducing the matrix

{R_{1} \to \frac{R_{1}}{2}} [\begin{matrix} 1 & 1.5 \\ 5 & 7 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5.5 \\ 24 \end{matrix}] {R_{2} \to R_{2} - 5 R_{1}} [\begin{matrix} 1 & 1.5 \\ 0 & - 0.5 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5.5 \\ - 3.5 \end{matrix}] {R_{2} \to - 2 R_{2}} [\begin{matrix} 1 & 1.5 \\ 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 5.5 \\ 7 \end{matrix}] {R_{1} \to R_{1} - 5 R_{2}} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} - 5 \\ 7 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} - 5 \\ 7 \end{matrix}]

Step 4.The solution

The values of x and y are $- 5 & 7$

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Algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x + 3 y = 11 \\ 5 x + 7 y = 24 \end{cases}$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Conversion of equations

Step 3.Reduction of matrix

Step 4.The solution

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Algebraically solve each system of equations using any method you wish.2x+3y=115x+7y=24

Short Answer

Step by step solution

Step 1.Given information

Step 2.Conversion of equations

Step 3.Reduction of matrix

Step 4.The solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Algebraically solve each system of equations using any method you wish.
$\{\begin{cases} 2 x + 3 y = 11 \\ 5 x + 7 y = 24 \end{cases}$