Final answer:
To solve the system of equations using the linear combination method, multiply the equations to make the coefficients of either x or y the same, add or subtract the equations to eliminate one variable, solve for the remaining variable, and substitute the value back into one of the original equations. the primary topic
Step-by-step explanation:
To solve the system of equations using the linear combination method, we will multiply each equation by a constant so that the coefficients of either x or y are the same (but with opposite signs) in both equations.
This will allow us to add or subtract the equations to eliminate one variable and solve for the other.
Here are the steps:
Multiply the first equation by 2 to make the coefficients of x the same:
2(2x - 3y) = 2(13)
Multiply the second equation by 3 to make the coefficients of x the same:
3(3x + 2y) = 3(-4)
Add the two new equations together:
4x - 6y + 9x + 6y = 26 - 12
Simplify the equation:
13x = 14
Divide both sides of the equation by 13:
x = 14/13
Substitute the value of x into one of the original equations to find y:
2(14/13) - 3y = 13
28/13 - 3y = 13
-3y = 13 - 28/13
-3y = (13*13 - 28)/13
-3y = (169 - 28)/13
-3y = 141/13
y = (141/13) * (-1/3)
y = -141/39
Therefore, the solution to the system of equations is x = 14/13 and y = -141/39.