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

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Answer 1 · 2016-11-06T12:52:54

$x = \frac{15}{2}$ $x = 15/2$ and $y = - 8$ $y = -8$

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

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

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

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

$\frac{2 y}{2} = \frac{14 - 4 x}{2}$ $(2y)/2 = (14 - 4x)/2$

$y = 7 - 2 x$ $y = 7 - 2x$

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

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

$4 x + 21 - 2 x = 6$ $4x + 21 - 2x = 6$

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

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

$2 x = - 15$ $2x = -15$

$\frac{2 x}{2} = \frac{15}{2}$ $(2x)/2 = 15/2$

$x = \frac{15}{2}$ $x = 15/2$

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

$y = 7 - 2 (\frac{15}{2})$ $y = 7 - 2(15/2)$

$y = 7 - 15$ $y = 7 - 15$

$y = - 8$ $y = -8$

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