Solve the system of equations.2𝑥+3𝑦=8−2𝑦=−4Group of answer choices(1,2)(−1,−2)(−1,2)(1,−2)

1. Break Down the Problem

We have a system of equations:

1. $2x + 3y = 8$
2. $-2y = -4$

We need to solve these equations for $x$ and $y$.

2. Relevant Concepts

To solve a system of equations, we can use substitution or elimination. In this case, the second equation can be manipulated to find $y$.

3. Analysis and Detail

Step 1: Solve the second equation for $y$. $-2y = -4$ Dividing both sides by -2: $y = 2$

Step 2: Substitute $y = 2$ into the first equation $2x + 3y = 8$: $2x + 3(2) = 8$ $2x + 6 = 8$ Subtracting 6 from both sides: $2x = 2$ Dividing both sides by 2: $x = 1$

4. Verify and Summarize

We found:

• $x = 1$
• $y = 2$

Let's check if these values satisfy both original equations.

1. For the first equation: $2(1) + 3(2) = 2 + 6 = 8 \quad \text{(True)}$
2. For the second equation: $-2(2) = -4 \quad \text{(True)}$

Final Answer

The solution to the system of equations is $(1, 2)$.