3r – 2s = 0
2r + 3s = 13
I know that it is m= yx+b I got that much but I don’t know where to go from here.
Use the elimination method to find the solution system.
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant to make the coefficients of either 'r' or 's' the same. In this case, it's convenient to make the coefficients of 's' the same.
To do that, we can multiply the first equation by 3 and the second equation by 2:
(3r – 2s) * 3 = 0 * 3
(2r + 3s) * 2 = 13 * 2
Simplifying the equations gives us:
9r - 6s = 0
4r + 6s = 26
Step 2: Add or subtract the equations to eliminate one variable. In this case, we'll eliminate 's'.
Adding the two equations gives us:
(9r - 6s) + (4r + 6s) = 0 + 26
Simplifying the equation gives us:
13r = 26
Step 3: Solve for the remaining variable. Divide both sides of the equation by 13:
13r / 13 = 26 / 13
r = 2
Step 4: Substitute the value of 'r' back into one of the original equations and solve for the remaining variable. Let's use the first equation:
3r - 2s = 0
Substituting r = 2 in the equation gives us:
3(2) - 2s = 0
6 - 2s = 0
Step 5: Solve for 's':
-2s = -6
s = 3
Therefore, the solution to the system of equations is r = 2 and s = 3.