Question

solving for systems of equations how do you work out -3x+4y=22, x-5y=-22

Answer 1

 

3x+4y=22, x-5y=-22

 

You can either solve by substitution method of elimination method.

 

Substitution method.

x - 5y = -22 iff

x = 5y - 22

 

We take the expression, 5y - 22, and substitute it in place of x in the other equation.

3x + 4y = 22

3(5y - 22) + 4y = 22 iff

15y - 66 + 4y = 22 iff

19y - 66 = 22 iff

19y = 88 iff

y = 88/19

 

Now plug in y = 88/19 into any of two equations and find x.

 

x = 5y - 22

x = 5(88/19) - 22

x = 22/19

 

Thus the solution to the system is (22/19, 88/19)

Answer 2

Elimination method.

Transform one or both equation so that a variable cancels out when combined together. Same as substitution method, we're trying to come up with one equation with only one variable.

 

Multiplying the second equation by -3,

 

-3(x - 5y = -22) --> -3x + 15y = 66

 

Combine this with the second equation.

 

3x + 4y = 22

-3x + 15y = 66

----------------------- add

19y = 88 iff

y = 88/19

 

Like before, plug in y = 88/19 into any of the two equations and solve for x.

 

x - 5y = -22

x - 5(88/19) = -22 iff

x = 22/19

 

Thus the solution is (22/19, 88/19), same as above.