Solve system of equation by cross …
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Sia ? 6 years, 5 months ago
Given equations are
mx - ny = m2 + n2 .................(i)
x + y = 2m ....................(ii)
Here
a1 = m, b1 = -n, c1 = -(m2 + n2)
a2 = 1, b2 = 1, c2 = -(2m)
By cross multiplication method
{tex}\frac{x}{{{{( 2mn + m^2 + n^2)} }}} = \frac{{ - y}}{{ - {2m^2} + m^2 + n^2 }} = \frac{1}{{m + n}}{/tex}
{tex}\frac{x}{{{{(m + n)}^2}}} = \frac{{ - y}}{{ - {m^2} + {n^2}}} = \frac{1}{{m + n}}{/tex}
Now, {tex}\frac{x}{{{{(m + n)}^2}}} = \frac{1}{{m + n}} {/tex}
{tex}⇒ x = m + n{/tex}
And, {tex}\frac{{ - y}}{{ - {m^2} + {n^2}}} = \frac{1}{{m + n}}{/tex}
{tex} ⇒ y = m - n{/tex}
The solutions of the given pair of equations are x = m + n and y = m - n.
0Thank You