Question

Solve the system of equations. 3x+6y=21. -5x+2y=13

Answer 1

To solve the system of equations, we can use either the substitution method or the elimination method.
Here, let's use the elimination method to solve the system of equations:
To eliminate x, we need to multiply the first equation by 5, and the second equation by 3:
5*(3x + 6y) = 5*21
3*(-5x + 2y) = 3*13
Which simplifies to:
15x + 30y = 105
-15x + 6y = 39
Adding the two equations together, we get:
(15x + 30y) + (-15x + 6y) = 105 + 39
36y = 144
Dividing both sides by 36, we get:
y = 4
Now, substitute the value of y into either of the original equations. Let's use the first equation:
3x + 6(4) = 21
3x + 24 = 21
Subtracting 24 from both sides, we get:
3x = -3
Dividing both sides by 3, we get:
x = -1
Therefore, the solution to the system of equations is x = -1 and y = 4.