Question

\begin{aligned}
&y=5x+2
\\\\
&4x-y=0
\end{aligned}

Answer 1

To solve the system of equations given by

1. \( y = 5x + 2 \)
2. \( 4x - y = 0 \)

we can substitute the expression for \( y \) from the first equation into the second equation.

Starting with the second equation, we can rewrite it as:

\[
y = 4x
\]

Now, we have two expressions for \( y \):

1. \( y = 5x + 2 \)
2. \( y = 4x \)

We can set these two equations equal to each other:

\[
5x + 2 = 4x
\]

Now, subtract \( 4x \) from both sides:

\[
5x - 4x + 2 = 0
\]

This simplifies to:

\[
x + 2 = 0
\]

Now, solve for \( x \):

\[
x = -2
\]

Next, we substitute \( x = -2 \) back into one of the original equations to find \( y \). We'll use the first equation:

\[
y = 5(-2) + 2
\]

Calculating this gives:

\[
y = -10 + 2 = -8
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, -8)
\]