emancipezN

2021-01-19

-In the system of equations in x and y, 2x+3y=12, 4x+ay=16, where a is an integer, what would a have to be for the equations to be inconsistent?

-In the system of equations in x and y, 2x+3y=12, 4x+ay=b, where a is the answer to question 2, what would b be if the equations are dependent?

-In the system of equations in x and y, 2x+3y=12, 4x+ay=b, where a is the answer to question 2, what would b be if the equations are dependent?

Willie

Skilled2021-01-20Added 95 answers

Step 1

To find value of a such that the system of equations 2x+3y=124x+ay=16 is inconsistent.

Using this value of a, to find value of b such that the system of equations 2x+3y=124x+ay=b is dependent.

Step 2

Let the system of equations be

${a}_{1}x+{b}_{1}y+{c}_{1}=0$

${a}_{2}x+{b}_{2}y+{c}_{2}=0$

$\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}\ne \frac{{c}_{1}}{{c}_{2}}$

Thus, for given system of equations

$\frac{2}{4}=\frac{3}{a}\ne -\frac{12}{-16}$

$\frac{1}{2}=\frac{3}{a}$

a=6

Step 3

System of equations is dependent, if

$\frac{{a}_{1}}{{a}_{2}}=\frac{{b}_{1}}{{b}_{2}}=\frac{{c}_{1}}{{c}_{2}}$

Thus, for given system of equations

$\frac{2}{4}=\frac{3}{a}=-\frac{12}{-b}$

$=\frac{3}{6}=\frac{12}{b}$

$\frac{1}{2}=\frac{12}{b}$

b=24

To find value of a such that the system of equations 2x+3y=124x+ay=16 is inconsistent.

Using this value of a, to find value of b such that the system of equations 2x+3y=124x+ay=b is dependent.

Step 2

Let the system of equations be

Thus, for given system of equations

a=6

Step 3

System of equations is dependent, if

Thus, for given system of equations

b=24

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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