Question

Choose the equation that combines with the following equation to create a system of linear equations with infinitely many solutions? 113x=53y−2

Answer 1

I can't see a list but any equation which is a multiple  of the given equation would do.

For example we could multiply each term in the equation by 2 to give:-

226x = 106y - 4.

Answer 2

Answer:

B.$22x=10y-12$

D.$11x=5y-6$

Step-by-step explanation:

We are given that an equation

$\frac{11}{3}x=\frac{5}{3}y-2$

We have to find the equation that combines with the given equation to create a system of linear equations with infinitely many solutions.

Condition of infinitely many solutions:

$a_1x+b_1y+c_1=0$

$a_2x+b_2y+c_2=0$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

A.$33x=15y-16$

$\frac{11}{3}x-\frac{5}{3}y+2=0$

$33x-15y+16=0$

$a_1=\frac{11}{3},b_1=-\frac{5}{3},c_1=2$

$a_2=33,b_2=-15,c_2=16$

$\frac{a_1}{a_2}=\frac{\frac{11}{3}}{33}=\frac{1}{9}$

$\frac{b_1}{b_2}=\frac{-\frac{5}{3}}{-15}=\frac{1}{9}$

$\frac{c_1}{c_2}=\frac{2}{16}=\frac{1}{8}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$

Hence, it is false.

B.$22x=10y-12$

$22x-10y+12=0$

$\frac{a_1}{a_2}=\frac{\frac{11}{3}}{22}=\frac{1}{6}$

$\frac{b_1}{b_2}=\frac{-\frac{5}{3}}{-10}=\frac{1}{6}$

$\frac{c_1}{c_2}=\frac{2}{12}=\frac{1}{6}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Hence, it is true.

C.$10x=4y-5$

$10x-4y+5=0$

$\frac{\frac{11}{3}}{10}=\frac{11}{30}$

$\frac{-\frac{5}{3}}{-4}=\frac{5}{12}$

$\frac{11}{130}\neq\frac{5}{12}$

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

Hence, it is not true.

D.$11x=5y-6$

$11x-5y+6=0$

$\frac{\frac{11}{3}}{11}=\frac{1}{3}$

$\frac{-\frac{5}{3}}{-5}=\frac{1}{3}$

$\frac{2}{6}=\frac{1}{3}$

$\therefore\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Hence, it is true.