Solve the pair of equations: 2x – 3y = -10, 10x – 6y = -5

Explanation

Step 1: Check if equations are parallel
Multiply first equation by 2:
2(2x – 3y) = 2(-10)
4x – 6y = -20

Step 2: Compare with second equation
First (multiplied): 4x – 6y = -20
Second: 10x – 6y = -5

Step 3: Check coefficient ratios
For parallel lines with no solution:
Ratio of x coefficients: 2/10 = 1/5
Ratio of y coefficients: -3/-6 = 1/2
Since 1/5 ≠ 1/2, lines are not parallel

Step 4: Alternative check – multiply equation 1 by 5
5(2x – 3y) = 5(-10)
10x – 15y = -50
Compare with 10x – 6y = -5

Step 5: Subtract to find y
(10x – 15y) – (10x – 6y) = -50 – (-5)
-9y = -45
y = 5
Then 2x – 15 = -10, so 2x = 5, x = 2.5
Check in second: 10(2.5) – 6(5) = 25 – 30 = -5 ✓
Wait – this DOES have solution! Answer key may be incorrect.