Which ordered pair is the solution to this system of eque $\newline$ $\left\{\begin{array}{c} x=\frac{1}{2} y+5 \\ 2 x+3 y=-14 \end{array}\right.$

Full solution

Q. Which ordered pair is the solution to this system of eque

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\left\{\begin{array}{c} x=\frac{1}{2} y+5 \\ 2 x+3 y=-14 \end{array}\right.

Express $x$ in terms of $y$ : We have the system of equations: $\newline$ $1$ . $x = \frac{1}{2}y + 5$ $\newline$ $2$ . $2x + 3y = -14$ $\newline$ First, let's express $x$ from the first equation in terms of $y$ .
Substitute and eliminate $x$ : Now, substitute the expression for $x$ from the first equation into the second equation to eliminate $x$ and solve for $y$ . $2\left(\frac{1}{2}y + 5\right) + 3y = -14$
Distribute and combine terms: Distribute the $2$ on the left side of the equation: $\newline$ $2\left(\frac{1}{2}\right)y + 2\cdot 5 + 3y = -14$ $\newline$ $y + 10 + 3y = -14$
Solve for y: Combine like terms: $\newline$ $y + 3y = -14 - 10$ $\newline$ $4y = -24$
Substitute $y$ back into first equation: Divide both sides by $4$ to solve for $y$ : $\frac{4y}{4} = \frac{-24}{4}$ $y = -6$
Find x value: Now that we have the value of $y$ , we can substitute it back into the first equation to solve for $x$ : $x = \left(\frac{1}{2}\right)(-6) + 5$
Final ordered pair: Perform the multiplication and addition to find $x$ : $x = -3 + 5$ $x = 2$
Final ordered pair: Perform the multiplication and addition to find $x$ : $x = -3 + 5$ $x = 2$ We have found the values of $x$ and $y$ that satisfy the system of equations. The ordered pair is $(2, -6)$ .