Question

Use algebraic rules of equations to predict the solution type to the system of equations. Include all of your work for full credit. x + 2y = 10 6y = -3x + 30

Answer 1

So is this one solution, no solutions, or infinite solutions?

Answer 2

Answer: infinitely many solutions

Explanation: 6y = -3x + 30 rewrites to 3x + 6y = 30

1. align equations x + 2y = 10

3x + 6y = 30

2. multiply first equation by -3 to get -3x - 6y = -30

3. align equations -3x - 6y = -30

3x + 6y = 30

4. add the equations and you they cancel out, which means infinitely many solutions