Question 1014327
your solution is (2,1).


this means x = 2 and y = 1


your equations are:


ax + by = -7
2ax - 3by = 1


since you know the value of x and y, you can replace x and y with their values in those equations.


when x = 2 and y = 1, the equations of:


ax + by = -7
2ax - 3by = 1


become:


2a + 1b = -7
4a - 3b = 1


the two equations you have to work with are now:


2a + 1b = -7
4a - 3b = 1


multiply both sides of the first equation by 2 and leave the second equation as is to get:


4a + 2b = -14
4a - 3b = 1


subtract the second equation from the first equation to get:


5b = -15


solve for b to get b = -3


in the first original equation, solve for a to get:


first original equation is 2a + 1b = -7
when b = -3, this equation becomes 2a - 3 = -7
add 3 to both sides of the equation to get 2a = -4
solve for a to get a = -2


you have a = -2 and b = -3


go back to your original equations and replace a with -2 and b with -3.


your original equations are:


ax + by = -7
2ax - 3by = 1


when a = -2 and b = -3, these equations become:


-2x -3y = -7
-4x + 9y = 1


to confirm that your values of a and b are correct, solve these two equations for x and y.


you should get x = 2 and y = 1


start with:


-2x - 3y = -7
-4x + 9y = 1


multiply both sides of the first equation by 2 and leave the second equation as is to get:


-4x - 6y = -14
-4x + 9y = 1


subtract the second equation from the first to get:


-15y = -15


solve for y to get y = 1.


go back to your original first equation and solve for x.


your first original equation in this series is -2x - 3y = -7
when y = 1, this equation becomes -2x - 3 = -7
add 3 to both sides of this equation to get -2x = -4
divide both sides of this equation by -2 to get x = 2


you get x = 2 and y = 1 as you should, since that's the value of x and y that you started with when solving for a and b.


your solution is:


a = -2
b = -3