To solve the system of equations in part a, we can use the method of elimination. By adding the two equations together, we can eliminate the variable y. The resulting equation is:
3x + y + (-2x - y) = 12 + (-26)
Combining like terms, we get:
x = -14
Substituting this value of x into one of the original equations, we can solve for y:
3(-14) + y = 12
-42 + y = 12
y = 54
Therefore, the solution to the system of equations is x = -14 and y = 54.
In part b, we can use the same method of elimination. By multiplying the second equation by 4 and adding it to the first equation, we can eliminate the variable y. The resulting equation is:
4x - 12y + (4)(11x - 11y) = 17 + (4)(22)
Combining like terms, we get:
15x = 101
x = 101/15
Substituting this value of x into one of the original equations, we can solve for y:
4(101/15) - 12y = 17
404/15 - 12y = 17
-12y = 17 - 404/15
-12y = -23/15
y = (-23/15)(-1/12)
y = 23/180
Therefore, the solution to the system of equations is x = 101/15 and y = 23/180.
In part c, the system of equations is inconsistent and has no solution.
Final answer is To solve the system of equations a) 3x + y = 12, -2x - y = -26, add the two equations together to eliminate y. Solve for x and substitute the value of x into one of the original equations to solve for y. The solution is x = -14 and y = 54. In b) 4x - 12y = 17, 11x - 11y = 22, multiply the second equation by 4 and add it to the first equation to eliminate y. Solve for x and substitute the value of x into one of the original equations to solve for y. The solution is x = 101/15 and y = 23/180. In c) 18x + 4y = -1, there is no solution.