Question

that applyProvide a complete written response to the prompts. You must include any graphs or sketchesI1. Explain how the points of intersection of graphs of functions can be determined (orverified) using the multiple representations of a system of equations. Provide examples anda sketch.

Answer 1

Given two linear equations:

y = -2.5x + 5

and

y = x - 0.5

You can find the solution (points of intersection of graphs) by forming a 2x2 system of equations and solving it

First, let's rewrite the equations in their standard form:

ax + by = c

So:

y = -2.5x + 5

Add 2.5x to both sides:

y + 2.5x = -2.5x + 5 + 2.5x

2.5x + y = 5

now, for the other equation:

y = x - 0.5

Subtract y from both sides:

y - y = x - 0-5 - y

x - y - 0.5 = 0

Add 0.5 to both sides

x - y -0.5 + 0.5 = 0.5

x - y = 0.5

Now, let:

2.5x + y = 5 (1)

x - y = 0.5 (2)

Let's use substitution method in order to solve this system:

From (1) let's solve for x:

2.5x = 5 - y

x = 2 - 0.4y (3)

Replace (3) into (2)

2 - 0.4y - y = 0.5

2 - 1.4y = 0.5

-1.4y = -1.5

y = 1.07

Replacing y into (3)

x = 2 - 0.4(1.07)

x = 1.57