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3 years ago

Write the word sentence as an inequality A number y divided by 6 is no more than 2

Mathematics

1 answer:

Sedbober [7]3 years ago

8 0

Answer:

Y/6 <_ 2

Step-by-step explanation:

(Less than it equal to sign)

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Find all solutions of the given system of equations (If the system is infinite many solution, express your answer in terms of x)

lisov135 [29]

Answer:

(a) The system of the equations $\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.$ has no solution.

(b) The system of the equations $\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.$ has many solutions $y=\frac{2x}{3}-\frac{5}{3}$

Step-by-step explanation:

(a) To find the solutions of the following system of equations $\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.$ you must:

Multiply $2x-3y=3$ by 2:

$\begin{bmatrix}4x-6y=6\\ 4x-6y=3\end{bmatrix}$

Subtract the equations

$4x-6y=3\\-\\4x-6y=6\\------\\0=-3$

0 = -3 is false, therefore the system of the equations has no solution.

(b) To find the solutions of the system $\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.$ you must:

Isolate x for $4x-6y=10$

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

Substitute $x=\frac{5+3y}{2}$ into the second equation

$16\cdot \frac{5+3y}{2}-24y=40\\8\left(3y+5\right)-24y=40\\24y+40-24y=40\\40=40$

The system has many solutions.

Isolate y for $4x-6y=10$

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

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3 years ago