Solve the system of equations.𝑦=5−2𝑥4𝑥+3𝑦=−13Group of answer choices(14,23)(−14,23)(14,−23)(−14,−23)

1. Break Down the Problem

We have the following system of equations:

1. $y = 5 - 2x$
2. $4x + 3y = -13$

We'll substitute the expression for $y$ from the first equation into the second equation to solve for $x$.

2. Relevant Concepts

We will use substitution to eliminate $y$ from the second equation.

3. Analysis and Detail

1. Substitute $y$ from the first equation into the second equation: $4x + 3(5 - 2x) = -13$

2. Simplify the equation: $4x + 15 - 6x = -13$ $-2x + 15 = -13$

3. Isolate $x$: $-2x = -13 - 15$ $-2x = -28$ $x = 14$

4. Now substitute $x = 14$ back into the first equation to find $y$: $y = 5 - 2(14)$ $y = 5 - 28$ $y = -23$

4. Verify and Summarize

We have found $x = 14$ and $y = -23$. Let's verify by substituting both values back into the second equation: $4(14) + 3(-23) = -13$ $56 - 69 = -13 \rightarrow -13 = -13 \text{ (True)}$ Both equations are satisfied.

Final Answer

The solution of the system of equations is $(14, -23)$.