Chapter 6.4, Problem 18PPS

To determine

To solve the given system of equations using elimination method

Answer to Problem 18PPS

$x=\frac{1}{2}$ and $y=1$

Explanation of Solution

Given:

Equations:

$-4x+2y=0$

$10x+3y=8$

Calculation:

Let,

$\begin{array}{l}-4x+2y=\mathrm{0.......}(i)\\ 10x+3y=\mathrm{8.......}(ii)\end{array}$

Now, subtract equation $2\times$ ( ii ) from $3\times$ equation ( i ),

$\begin{array}{l}\Rightarrow 3\times (-4x+2y)-2\times (10x+3y)=3\times (0)-2\times (8)\\ \Rightarrow -12x+6y-20x-6y=-16\\ \Rightarrow -32x=-6\\ \Rightarrow x=\frac{1}{2}\end{array}$

Now, substitute the value of x in equation ( i ),

$\begin{array}{l}\Rightarrow -4\times (\frac{1}{2})+2y=0\\ \Rightarrow y=1\end{array}$

Conclusion:

Therefore, the required solution for the given system of equation is $x=\frac{1}{2}$ and $y=1$ .