Question

if x+2y=7 and 4x-ay=10 has no solutions then a

Answer 1

x+2y-7=0;and4x-ay-10=0
for no solution a1/a1=b1/b 2 does not equal to c1/c2
1/4=2/-a
-a=8
hence a=-8

Answer 2

The correct answer is -8.

Given: Equations = x+2y=7 and 4x-ay=10.

To Find: Value of a for no solution condition.

Solution:

In the equations $a_{1} x^{2} +b_{1} x+c_{1} =0$ and $a_{2} x^{2} +b_{2} x+c_{2} =0$.

The condition of no solution = $\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }$.

So, apply the condition in the given equations x+2y-7 = 0 and 4x-ay-10=0.

$\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } \neq \frac{c_{1} }{c_{2} }$

$\frac{1}{4} =\frac{2}{-a} \neq \frac{-7}{-10}$

Take first two terms.

$\frac{1}{4} =\frac{2}{-a}$

-a = 8

a = -8

Take last two terms.

$\frac{2}{-a} \neq \frac{-7}{-10}$

$a\neq -\frac{20}{7}$

Hence, the value of a is -8.

#SPJ2