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A set of equations is given below: Equation C: y = 5x + 10 Equation D: y = 5x + 2 Which of the following best describes the solution to the given set of equations?



One solution No solution Two solutions Infinitely many solutions

Verified Answer :

Petroniusz

The system of equations
 \(\left \{ {{y = 5x + 10 } \atop { y = 5x + 2}} \right.\) 


you can easily see that they are contrary to the equation . We not solve them .
However prove it.

by substitution .

We substitute the value of y from the first equation to the second equation

y = 5x + 10
y = 5x + 2

y = 5x + 10
5x + 10 = 5x  + 2

y = 5x + 10
5x - 5x = 2 - 10

y = 5x + 10
0  ≠ -8

or by opposing coefficients
y = 5x + 10  [* (-1)
y = 5x + 2

-y = -5x - 10
y = 5x + 2
----------------- sum
0 ≠ -8

Answer.  No solution

The system of equations has no solution.

What is equation?

An equation is arrangement of variables and coefficient which provides to understand given statement in form of numbers .That means a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

How to solve?

Given equation y=5x+10 and other equation y=5x+2

to check if two have any solution possible we will substitute value and check if RHS=LHS or not

∴y=5x+10=5x+2

=5x+10=5x+2

⇒0= -8

hence RHS≠ LHS hence no solution is possible

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