Question

in exercises 1-6, describe how you would 1. $x + 4y = 30$ $x = 2y$

Explanation:

Step1: Substitute \( x = 2y \) into \( x + 4y = 30 \)

Since we know \( x \) is equal to \( 2y \), we can replace \( x \) in the first equation with \( 2y \). So we get \( 2y + 4y = 30 \).

Step2: Simplify the left - hand side

Combine like terms: \( 2y+4y=(2 + 4)y = 6y \). So the equation becomes \( 6y=30 \).

Step3: Solve for \( y \)

Divide both sides of the equation \( 6y = 30 \) by 6. \( y=\frac{30}{6}=5 \).

Step4: Solve for \( x \)

Substitute \( y = 5 \) into the equation \( x = 2y \). Then \( x=2\times5 = 10 \).

Answer:

The solution of the system of equations \(

$$\begin{cases}x + 4y=30\\x = 2y\end{cases}$$

\) is \(x = 10\) and \(y = 5\).