To solve a system of simultaneous linear equations using the elimination method, you need to eliminate one variable by adding or subtracting the equations in the system to find the values of x and y that satisfy both equations.
Let's look at each system provided and solve them step by step:
1.
(x+y=5)
(x-y=3)
Adding the two equations:
x + y = 5
x - y = 3
-----------------
2x = 8
x = 4
Substitute x back into one of the original equations:
4 + y = 5
y = 1
Therefore, the solution is x = 4, y = 1.
2.
(11x-8y=27)
(3x-2y=19)
Multiply the second equation by 4 to have the same coefficient for y:
(11x-8y=27)
(12x-8y=76)
Subtract the second equation from the first:
-x = -49
x = 49
Substitute x back into one of the original equations:
4(49) + y = 18
196 + y = 18
y = -178
Therefore, the solution is x = 49, y = -178.
3.
(4x-3y=18)
(6x + 7y = 4)
Multiply the first equation by 7 and the second equation by 3 to eliminate y:
(28x - 21y = 126)
(18x + 21y = 12)
Add the two equations:
46x = 138
x = 3
Substitute x back into one of the original equations:
4(3) - 3y = 18
12 - 3y = 18
-3y = 6
y = -2
Therefore, the solution is x = 3, y = -2.
4. (Not enough information provided to solve)
