Question

Find the ordered pair $(x,y)$ that satisfies the system of equations

\begin{align*}
2x + y &=-7,\\
x &=4+2y.
\end{align*}

Answer 1

Using substitution method, we solve the system of linear equations to find the ordered pair $(-2,-3)$ that satisfies both equations.

Step-by-step explanation:

To find the ordered pair $(x,y)$ that satisfies the given system of linear equations:

1. $2x + y = -7$
2. $x = 4 + 2y$

We will employ the substitution method. First, we'll express $x$ in terms of $y$ using the second equation and then substitute that expression into the first equation.

• From the second equation, $x = 4 + 2y$.
• Substitute $x$ into the first equation: $2(4 + 2y) + y = -7$.
• Simplify and solve for $y$: $8 + 4y + y = -7$ which simplifies to $5y = -15$.
• Divide by 5 to find $y$: $y = -3$.
• Substitute $y$ back into $x = 4 + 2y$ equation to find $x$: $x = 4 + 2(-3)$.
• Calculate $x$: $x = 4 - 6$.
• Therefore, $x = -2$.

So, the solution to the system is the ordered pair $(-2,-3)$.