Question

Using the equation y=2/3x-5, describe how to create a system of linear equations with an infinite number of solutions.

Answer 1

a system of linear equations with infinite solutions, is simply one that has the same equation twice, but but but, one of the equations is in disguise.

so, say we can just  hmmm multiply the coefficient of the "x" variable, which is the slope, by something that gives us 1, recall same/same = 1, hmmm say let's multiply it by hmmmm 7/7.

$\bf y=\cfrac{2}{3}x-5\implies \stackrel{\textit{multiplying the slope by }\frac{7}{7}}{\cfrac{2}{3}\cdot \cfrac{7}{7}\implies \cfrac{14}{21}}\implies \stackrel{\textit{so we get this equation}}{y=\cfrac{14}{21}x-5}$

now, let's notice that 14/21 simplifies to 2/3, so is really the same slope and the same y-intercept.

so if we use those two equations in a system of equations and graph them, what happens is, the first one will graph a line, the second one will graph another line BUT right on top of the first one drawn, so the two lines will just be pancaked on top of each other, making every point in each line, "a solution", since they're meeting at every point, and since lines go to infinite, "infinitely many solutions".

Answer 2

Answer:

Sample Response/Explanation: To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.

Step-by-step explanation: