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Q. 27

Expert-verifiedFound in: Page 714

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Solve each system of equations. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{c}2x-y=0\\ 4x+2y=12\end{array}\right.$

The solution of the given system of equation is $x=1.5,y=3,(1.5,3)$.

The given equations are:

$\begin{array}{rcl}2x-y& =& 0\\ 4x+2y& =& 12\end{array}$

The first equation can be written as:

$\begin{array}{rcl}2x-y& =& 0\\ -y& =& -2x\\ y& =& 2x\end{array}$

Substitute the above value in the second equation.

$\begin{array}{rcl}4x+2\left(2x\right)& =& 12\\ 4x+4x& =& 12\\ 8x& =& 12\\ x& =& \frac{12}{8}\\ x& =& 1.5\end{array}$

Substitute $x=1.5$ in $y=2x$.

$y=2(1.5)\phantom{\rule{0ex}{0ex}}y=3$

The solution of the given system of equation is $x=1.5,y=3,(1.5,3)$.

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