Question

Solve the system of equation algebraically

6x-3y=-33

2x+y=-1

Answer 1

To solve the system of equations algebraically, we can use the method of substitution or elimination.

1. Method of Substitution:
We can solve one equation for one variable and substitute it into the other equation.
From the second equation, we can isolate y:
2x + y = -1
y = -2x - 1

Substitute this value of y into the first equation:
6x - 3(-2x - 1) = -33
6x + 6x + 3 = -33
12x + 3 = -33
12x = -36
x = -3

Substitute the value of x into the second equation to find y:
2(-3) + y = -1
-6 + y = -1
y = 5

The solution to the system of equations is x = -3 and y = 5.

2. Method of Elimination:
We can multiply the second equation by 3 and add it to the first equation to eliminate y.

6x - 3y = -33
2x + y = -1

Multiply the second equation by 3:
6x + 3y = -3

Add the multiplied second equation to the first equation:
6x - 3y + 6x + 3y = -33 + (-3)
12x = -36
x = -3

Substitute the value of x into the second equation to find y:
2(-3) + y = -1
-6 + y = -1
y = 5

The solution to the system of equations is x = -3 and y = 5.

Therefore, the system of equations is solved algebraically and the solution is x = -3 and y = 5.