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

Answer 1

To solve the system of equations:

3x + 6y = 21 ...(Equation 1)
-5x + 2y = 13 ...(Equation 2)

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

Let's use the method of substitution:

From Equation 1, we can express x in terms of y:
3x = 21 - 6y
Dividing both sides by 3:
x = 7 - 2y/3 ...(Equation 3)

Now, substitute x = 7 - 2y/3 into Equation 2:
-5(7 - 2y/3) + 2y = 13
Expanding:
-35 + 10y/3 + 2y = 13
Multiplying both sides by 3 to eliminate the fraction:
-105 + 10y + 6y = 39
Combining like terms:
16y = 144
Dividing both sides by 16:
y = 9

Now, substitute y = 9 back into Equation 3 to find x:
x = 7 - 2(9)/3
x = 7 - 6
x = 1

Therefore, the solution to the system of equations is x = 1 and y = 9.