write two other equations that have the same solution as this system od equations.
3x-4y=-14
-x+3y=18
I found the solution to the system it is (6,8) there after how do i go about it?
Just make up any old left-side of an equation.
e.g. 5x - 2y = ??
now plug in your values to get
30 - 16 = 14
so one equation is 5x - 2y = 14
as you can see there would be an infinite number of equations you could form
x-4y=-2
5x-y=-3
2x+y+z=0,x+y+2z=0,5x+3y+3z=2
x=-2,y=6,z=-2
To find two other equations that have the same solution as the given system of equations, you can use the concept of equivalent equations.
Step 1: Start with the given system of equations:
3x - 4y = -14 ...(Equation 1)
-x + 3y = 18 ...(Equation 2)
Step 2: Choose any equation and manipulate it to get an equivalent equation. Let's choose Equation 1 and manipulate it by multiplying both sides by -1:
-1(3x - 4y) = -1(-14)
-3x + 4y = 14 ...(Equation 3)
Step 3: Choose another equation and manipulate it to get an equivalent equation. Let's choose Equation 2 and manipulate it by multiplying both sides by 2:
2(-x + 3y) = 2(18)
-2x + 6y = 36 ...(Equation 4)
Now, Equations 3 and 4 are two other equations that have the same solution as the original system of equations.
In general, any equation that is obtained by multiplying both sides of a given equation by the same non-zero constant or adding to/subtracting from both sides of a given equation by the same quantity will be an equivalent equation with the same solution.
To verify that the solution to the original system is (6,8), substitute x = 6 and y = 8 into both Equation 1 and Equation 2:
For Equation 1:
3(6) - 4(8) = -14
18 - 32 = -14
-14 = -14 (True)
For Equation 2:
-(6) + 3(8) = 18
-6 + 24 = 18
18 = 18 (True)
Since both Equation 1 and Equation 2 are satisfied when x = 6 and y = 8, the solution (6,8) is correct.