Question

solve the following system of linear equations by using substitution. write your answer as an ordered pair.\

$$\begin{cases}x + y = 15 \\\\ y = 4x\\end{cases}$$

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answer

Explanation:

Step1: Substitute \( y = 4x \) into \( x + y = 15 \)

We know that \( y = 4x \), so we can replace \( y \) in the first equation with \( 4x \). This gives us the equation \( x + 4x = 15 \).

Step2: Solve for \( x \)

Combine like terms on the left side: \( 5x = 15 \). Then, divide both sides by 5: \( x=\frac{15}{5}=3 \).

Step3: Solve for \( y \)

Now that we know \( x = 3 \), we substitute \( x = 3 \) back into the equation \( y = 4x \). So, \( y = 4\times3 = 12 \).

Answer:

\((3, 12)\)