Use the elimination method to solve the sysrem of equations
a+6b=13
a+3b=4
a+6b=13
a+3b=4
----------subtract
0a+3b = 9
b = 3
then
a + 9 = 4
a = -5
To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. Let's start by eliminating the variable "a."
Given equations:
1) a + 6b = 13
2) a + 3b = 4
To eliminate "a," we can subtract equation 2 from equation 1:
(a + 6b) - (a + 3b) = 13 - 4
This simplifies to:
3b = 9
Now, we can solve for "b" by dividing both sides of the equation by 3:
3b/3 = 9/3
b = 3
Now that we have found the value of "b," we can substitute it back into one of the original equations to solve for "a." Let's substitute "b = 3" into equation 2:
a + 3(3) = 4
a + 9 = 4
Next, we can isolate "a" by subtracting 9 from both sides of the equation:
a + 9 - 9 = 4 - 9
a = -5
Therefore, the solution to the system of equations is:
a = -5 and b = 3.