Chapter 3: Q48. (page 135)

Solve each system of equations by using either substitution or elimination
$\begin{matrix} 4 x + 5 y = 20 \\ 5 x + 4 y = 7 \end{matrix}$

Short Answer

Expert verified

The solution of the system of equations is $(x, y) = (- 5, 8)$ .

Step by step solution

– Apply elimination method to solve the system of equations.

Elimination method enables us to eliminate or get rid of one of the variable, so we can solve a more simplified equation.

– Evaluate the system of equations

Given system of equations:

$\begin{matrix} 4 x + 5 y = 20 \\ 5 x + 4 y = 7 \end{matrix}$

Multiply the first equation, $4 x + 5 y = 20$ by 5 and second equation, $5 x + 4 y = 7$ by 4.

Then subtract the equations to eliminate the x variable as follows:

localid="1648726261833" $\begin{array}{l} \underline{\begin{matrix} 4 x + 5 y = 20 \\ 5 x + 4 y = 7 \end{matrix}} \begin{matrix} multiplyby5 \to \\ multiplyby4 \to \end{matrix} \underline{\begin{matrix} 20 x + 25 y = 100 \\ \underline{20 x} + \underline{16 y} = \underline{28} \end{matrix}} \\ 0 x + 9 y = 72 \end{array}$

Solve the equation $9 y = 72$ for y:

$\begin{matrix} 9 y = 72 \\ \frac{9 y}{9} = \frac{72}{9} dividebothsidesby9 \\ y = 8 \end{matrix}$

– Find the value of x

Substitute $y = 8$ in $4 x + 5 y = 20$ and solve for $x :$

\begin{matrix} 4 x + 5 y = 20 \\ 4 x + 5 (8) = 20 substitute8for y \\ 4 x + 40 = 20 simplify \\ 4 x = - 20 subtract40frombothsides \\ x = - 5 dividebothsidesby4 \end{matrix}

So, the solution of the given system is $(x, y) = (- 5, 8)$ .

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Solve each system of equations by using either substitution or elimination
$\begin{matrix} 4 x + 5 y = 20 \\ 5 x + 4 y = 7 \end{matrix}$

Short Answer

Step by step solution

– Apply elimination method to solve the system of equations.

– Evaluate the system of equations

– Find the value of x

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Solve each system of equations by using either substitution or elimination4x+5y=205x+4y=7

Short Answer

Step by step solution

– Apply elimination method to solve the system of equations.

– Evaluate the system of equations

– Find the value of x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each system of equations by using either substitution or elimination
$\begin{matrix} 4 x + 5 y = 20 \\ 5 x + 4 y = 7 \end{matrix}$