Find two solution of the equation 4x+5y =28 check whether (-2,10) is solution of the given equatio

Answer

To solve the problem, we will follow these steps:

### Step 1: Check if (-2, 10) is a solution of the equation 4x + 5y = 28.

We will substitute x = -2 and y = 10 into the equation.

**Substitution:**
\[ 4(-2) + 5(10) \]

**Calculation:**
\[ = -8 + 50 \]
\[ = 42 \]

Now, we compare this with the right-hand side of the equation, which is 28.

**Conclusion:**
Since 42 ≠ 28, (-2, 10) is not a solution of the equation.

### Step 2: Find two solutions of the equation 4x + 5y = 28.

We can choose any value for x and solve for y, or vice versa.

**First Solution:**
Let’s choose \( x = 2 \).

**Substitution:**
\[ 4(2) + 5y = 28 \]

**Calculation:**
\[ 8 + 5y = 28 \]
Subtract 8 from both sides:
\[ 5y = 28 - 8 \]
\[ 5y = 20 \]
Now, divide by 5:
\[ y = 4 \]

So, the first solution is \( (2, 4) \).

**Second Solution:**
Now, let’s choose \( x = 7 \).

**Substitution:**
\[ 4(7) + 5y = 28 \]

**Calculation:**
\[ 28 + 5y = 28 \]
Subtract 28 from both sides:
\[ 5y = 28 - 28 \]
\[ 5y = 0 \]
Now, divide by 5:
\[ y = 0 \]

So, the second solution is \( (7, 0) \).

### Final Solutions:
The two solutions of the equation 4x + 5y = 28 are:
1. \( (2, 4) \)
2. \( (7, 0) \)

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