Solution of the linear equations $3x+2y=4$ and $8x+5y=9$ is

Q: Solution of the linear equations $3x+2y=4$ and $8x+5y=9$ is

To determine the solution of the linear equations $3x + 2y = 4$ and $8x + 5y = 9$, we need to find the values of $x$ and $y$ that satisfy both equations simultaneously. The correct answer is given as Option 2: $x = -2$, $y = 5$. Let's verify this and explain why this option is correct, while the others are not. ### Verification of Option 2: $x = -2$, $y = 5$ 1. **Substitute into the first equation:** \[ 3(-2) + 2(5) = -6 + 10 = 4 \] This satisfies the first equation $3x + 2y = 4$. 2. **Substitute into the second equation:** \[ 8(-2) + 5(5) = -16 + 25 = 9 \] This satisfies the second equation $8x + 5y = 9$. Since both equations are satisfied, Option 2 is indeed the correct solution. ### Explanation of why other options are incorrect: 1. **Option 1: $x = 2$, $y = 5$** - **First equation:** \[ 3(2) + 2(5) = 6 + 10 = 16 \neq 4 \] This does not satisfy the first equation. - **Second equation:** \[ 8(2) + 5(5) = 16 + 25 = 41 \neq 9 \] This does not satisfy the second equation. 2. **Option 3: $x = 5$, $y = 2$** - **First equation:** \[ 3(5) + 2(2) = 15 + 4 = 19 \neq 4 \] This does not satisfy the first equation. - **Second equation:** \[ 8(5) + 5(2) = 40 + 10 = 50 \neq 9 \] This does not satisfy the second equation. 3. **Option 4: $x = -5$, $y = -2$** - **First equation:** \[ 3(-5) + 2(-2) = -15 - 4 = -19 \neq 4 \] This does not satisfy the first equation. - **Second equation:** \[ 8(-5) + 5(-2) = -40 - 10 = -50 \neq 9 \] This does not satisfy the second equation. In conclusion, only Option 2, $x = -2$ and $y = 5$, satisfies both equations, confirming it as the correct solution.

Question

Accepted Answer

To determine the solution of the linear equations $3x + 2y = 4$ and $8x + 5y = 9$, we need to find the values of $x$ and $y$ that satisfy both equations simultaneously. The correct answer is given as Option 2: $x = -2$, $y = 5$. Let's verify this and explain why this option is correct, while the others are not.

### Verification of Option 2: $x = -2$, $y = 5$

1. **Substitute into the first equation:**
   $$
   3(-2) + 2(5) = -6 + 10 = 4
   $$
   This satisfies the first equation $3x + 2y = 4$.

2. **Substitute into the second equation:**
   $$
   8(-2) + 5(5) = -16 + 25 = 9
   $$
   This satisfies the second equation $8x + 5y = 9$.

Since both equations are satisfied, Option 2 is indeed the correct solution.

### Explanation of why other options are incorrect:

1. **Option 1: $x = 2$, $y = 5$**
   - **First equation:**
     $$
     3(2) + 2(5) = 6 + 10 = 16 \neq 4
     $$
     This does not satisfy the first equation.
   - **Second equation:**
     $$
     8(2) + 5(5) = 16 + 25 = 41 \neq 9
     $$
     This does not satisfy the second equation.

2. **Option 3: $x = 5$, $y = 2$**
   - **First equation:**
     $$
     3(5) + 2(2) = 15 + 4 = 19 \neq 4
     $$
     This does not satisfy the first equation.
   - **Second equation:**
     $$
     8(5) + 5(2) = 40 + 10 = 50 \neq 9
     $$
     This does not satisfy the second equation.

3. **Option 4: $x = -5$, $y = -2$**
   - **First equation:**
     $$
     3(-5) + 2(-2) = -15 - 4 = -19 \neq 4
     $$
     This does not satisfy the first equation.
   - **Second equation:**
     $$
     8(-5) + 5(-2) = -40 - 10 = -50 \neq 9
     $$
     This does not satisfy the second equation.

In conclusion, only Option 2, $x = -2$ and $y = 5$, satisfies both equations, confirming it as the correct solution.