Answered

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?


y = 2x – 5


2y – 4x =


–10

–5

5

10

Verified Answer :

topoisomerase

-10. One type of system of equations that results in infinite solutions is one where both sides of the equation are exactly equal. Here, setting the second equation equal to -10 becomes 2y - 4x = -10. This can be rearranged into 2y = 4x - 10. Dividing everything by 2 results in y = 2x - 5, which is exactly what the first equation is. Substituting one equation into another, we get 2x - 5 = 2x - 5, which is a true statement for all values of x.

When -10 is placed in the box that would result in a system of equations with infinitely many solutions.

What is system of equation?

"It is a finite system of equations for which we find the common solution."

What is y-intercept?

"It is the point at which the graph of the intersects the Y-axis."

For given equation,

Let 'm' be the solution of 2y - 4x

⇒ 2y - 4x = b

We write above equation in slope-intercept form.

⇒ 2y - 4x = b

⇒ 2y = b + 4x

⇒ 2y = 4x + b

\(\Rightarrow y=2x+\frac{b}{2}\)

The y-intercept of above equation is  \(\frac{b}{2}\).

Also for equation y = 2x – 5 from given system of equations has               y-intercept is -5.

We know, the system of an equation has infinitely many solutions when they have the same y-intercept.

\(\Rightarrow -5=\frac{b}{2}\\\\\Rightarrow \bold{b=-10}\)

Therefore, when -10 is placed in the box that would result in a system of equations with infinitely many solutions.

Learn more about system of equation here:

https://brainly.com/question/12895249

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