Question

Without graphing, determine whether the system of linear equations has one solution, infinitely many solutions, or no solution. Explain your reasoning.
$y=15x+1$
$y=15x+2$

Answer 1

$\huge{ \mathcal{ \underline{ Answer} \: \: ✓ }}$

First equation :

• $y = 15x + 1$

• $y - 15x - 1 = 0$

Second equation :

• $y = 15x + 2$

• $y - 15x - 2 = 0$

Now, the equations are in the form of

• $a_1x {}^{2} + b_1x + c_1 = 0$

• $a_2x {}^{2} + b_2x + c_2 = 0$

where,

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

therefore the equations would have no solution .

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