Solve the system of equations using either the substitution method or the multiplication/addition method
answer:
3x+2y=14
2x-4y=4
I would double the first then add that to the 2nd to get
8x = 32
x =4
sub into the first:
12 + 2y = 14
2y = 2
y = 1
x=4, y =1
check by subbing those values into both equations, they should work
thanks so much! do you know how i could check the solution by writing the system as a matrix equation and using the inverse matrix?
ahh thank you and sorry for the overkill
To solve the system of equations using the substitution method, we need to solve one of the equations for one variable and substitute it into the other equation.
Let's solve the first equation for x:
3x + 2y = 14
Rearranging the equation:
3x = 14 - 2y
x = (14 - 2y) / 3
Now substitute this expression for x into the second equation:
2x - 4y = 4
Substitute (14 - 2y) / 3 for x:
2((14 - 2y) / 3) - 4y = 4
Simplify and solve for y:
(28 - 4y) / 3 - 4y = 4
28 - 4y - 12y = 12
28 - 16y = 12
-16y = 12 - 28
-16y = -16
y = (-16) / (-16)
y = 1
Now substitute the value of y into the first equation to solve for x:
3x + 2(1) = 14
3x + 2 = 14
3x = 14 - 2
3x = 12
x = 12 / 3
x = 4
So the solution to the system of equations is x = 4 and y = 1.
Wow , that would be overkill, but anyway ....
first of all , it is very difficult to write it in matrix form in this format,
so you would have the matrix
3 2
2-4 multiplied by the column matrix
x
y
=
14
4
I will assume you know how to find the inverse of a 2by2 matrix, and how to multiply matrices
the inverse of our 2by2 is
1/4 1/8
1/8 -3/16
so
1/4 1/8
1/8 -3/16
multiplied by
14
4
gives us
4
1