Solve the system by substitution 3x + 2y = -11 x = -11 + 3y

Question

Algebra Substitution method

Answer 1

Substitute the value for x given by your second equation into the first equation for every instance of x you see:

 

since x=-11+3y

 

The LHS of the first equation becomes:

3x+2y=3(-11+3y)+2y

which we know must equal -11 by the first equality given...

 

so 3(-11+3y)+2y = -11

 

Multiplying and distributing the 3, gives us:

 

-33+9y+2y = -11, and grouping the y terms together

-33+11y = -11, now adding 33 to both sides and then dividing by 11, will produce a value for y

 

11y = 22, or y=2...

 

We can now plug this call for y back in to EITHER of the equations and solve for x

 

x = -11 + 3y = -11 + 3(2) = -11 + 6 = -5

 

so x=-5 and y=2 is the solution to the system of linear equations...we should check that we solved it correctly by plugging back in to the other equation

 

3(-5) + 2(2) does in fact equal -11, so our solution does satisfy both equations and is correct!

 

Hope that helps.