Question

If the system of equation 3×+2y-7=0 and k×+2y+11=o has unique solution then

Answer 1

Step-by-step explanation:

Given: 3x+2y-7=0 and kx+2y+11=0

To find: If the system of equation has unique solution then find k.

Solution:

Condition for unique solution of equations

$\boxed{\bold{\frac{a_1}{a_2}\neq\frac{b_1}{b_2}}}$

if $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ are linear equations.

Write values of coefficients for given equations,

$a_1 = 3 \\ b_1 = 2 \\ a_2 = k\\ b_2 = 2$

apply the condition to find the value of k

$\frac{3}{k} \neq \frac{2}{2} \\ \\ \frac{3}{k} \neq1 \\ \\ 3 \: \neq \: k$

Final answer:

$\bold{\red{k\neq3 }}$

for equations to have unique solution.

Hope it helps you.

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