How do you solve the system of equations: $4x + 2y = 14$ and $4x + 3y = 6$ ?

Question

6992 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-06T12:52:54

$x = 15/2$ and $y = -8$

Step 1) First solve the second equation for $y$ while keeping both sides of the equation balanced:

$4x + 2y = 14$

$4x + 2y - 4x = 14 - 4x$

$2y = 14 - 4x$

$(2y)/2 = (14 - 4x)/2$

$y = 7 - 2x$

Step 2) Substitute $7 - 2x$ for $y$ in the first equation and solve for $x$ while keeping both sides of the equation balanced:

4x + 3(7 - 2x) = 6#

$4x + 21 - 2x = 6$

$2x + 21 = 6$

$2x + 21 - 21 = 6 - 21$

$2x = -15$

$(2x)/2 = 15/2$

$x = 15/2$

Step 3) Substitute $15/2$ for $x$ in the solution for Step 1 to find $y$ :

$y = 7 - 2(15/2)$

$y = 7 - 15$

$y = -8$

How do you solve the system of equations: 4x + 2y = 144x + 2y = 14 and 4x + 3y = 64x + 3y = 6?