Question

What is the solution to the system of equations? 2x – y = 7 y = 2x + 3 (2, 3) (2, 7) no solution infinite number of solutions

Answer 1

Answer:

Option C.

Step-by-step explanation:

Let $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ are two line.

If $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$, then system of equations have infinite number of solutions.

If  $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$, then system of equations have no solution.

If $\dfrac{a_1}{a_2}\neq \dfrac{b_1}{b_2}$, then system of equations have unique solution.

The given equations are

$2x-y=7$

$y=2x+3$

These equations can be rewritten as

$2x-y-7=0$

$2x-y+3=0$

Here, $a_1=2,b_1=-1,c_1=-7,a_2=2,b_2=-1,c_2=3$.

$\dfrac{a_1}{a_2}=\dfrac{2}{2}=1$

$\dfrac{b_1}{b_2}=\dfrac{-1}{-1}=1$

$\dfrac{c_1}{c_2}=\dfrac{-7}{3}$

Since, $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}$, therefore, the system of equations have no solution.

Hence, option C is correct.

Answer 2

Answer:

C. No solutions

Step-by-step explanation:

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