Home › NY Regents Algebra I › Mathematics › Systems of Linear Equations › Solve by elimination: 3x - 2y = -2 and 5x - 6y =…
Solve by elimination: 3x - 2y = -2 and 5x - 6y = 10.
A(-4, -5)
B(-5, -4)
C(4, 5)
D(-4, 5)
Answer & Solution
Correct answer: A. (-4, -5)
1. Multiply the first equation by -3 to make the y-coefficients opposites: -9x plus 6y equals 6.
2. Add this to the second equation, 5x minus 6y equals 10: -4x equals 16, so x equals -4.
3. Substitute x = -4 into 3x - 2y = -2 to get -12 minus 2y equals -2, so y equals -5.
4. Check: 3(-4) minus 2(-5) equals -12 plus 10, which equals -2, matching the first equation.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.3 Solve Systems of Equations by Elimination_
Related questions
The perimeter of a rectangle is 40. The length is 4 more than the width. Find the length aThe sum of two numbers is 10. One number is 4 less than the other. Find the numbers.When Jenna spent 10 minutes on the elliptical and 20 minutes on circuit training, she burnA married couple together earns $110,000 a year. The wife earns $16,000 less than twice whDevon is 26 years older than his son Cooper. The sum of their ages is 50. Find their ages.In the seven-step Problem Solving Strategy for Systems of Linear Equations, what is Step 4Joe had one medium fries and two small sodas for 620 calories on Monday, and two medium frThe sum of two numbers is 39. Their difference is 9. Find the numbers.