9x+y=30 6x-y=15

Answer 1

We can solve this system of equations using elimination or substitution method.

Elimination method:

1. Multiply the first equation by 6 and the second equation by 1 to get:

54x + 6y = 180
6x - y = 15

2. Add the two equations together to eliminate y:

60x = 195

3. Solve for x:

x = 3.25

4. Substitute x = 3.25 into one of the original equations to solve for y:

9(3.25) + y = 30
y = 1.75

5. The solution is (x,y) = (3.25,1.75)

Substitution method:

1. Solve one of the equations for one variable in terms of the other:

y = 30 - 9x

2. Substitute this expression for y into the second equation:

6x - (30 - 9x) = 15

3. Simplify and solve for x:

15x = 45

x = 3

4. Substitute x = 3 into one of the original equations to solve for y:

9(3) + y = 30

y = 1.5

5. The solution is (x,y) = (3,1.5)

Both methods give the same solution of (3,1.5) or (3.25,1.75).