System of linear equations

Question

Without graphing, construct a system of two linear equations where (-2,3) is a solution to the first equation but not to the second equation, and where (5,-2) is a solution to your system 

Answer 1

Let's start by finding the slope of our first line:

(y₂ - y₁) / (x₂ - x₁) = m

(-2 - 3) / (5 - (-2)) = m

-5 / (5 + 2) = m

-⁵/₇ = m

 

Since we have a coordinate, we can use the point-slope formula:

y - y₁ = m(x - x₁)

y - 3 = -⁵/₇(x - (-2))

y - 3 = -⁵/₇(x + 2)

y - ²¹/₇ = -⁵/₇ x - ¹⁰/₇

y = -⁵/₇ x + ¹¹/₇

 

That's the linear equation for your first line. Now to look at your second, let's return to the point-slope equation:

y - (-2) = m(x - 5)

y + 2 = m(x - 5)

 

From here, you will need to create your own slope (m) and make it different from the -5/7 from the first equation so that you have two separate lines. If you want to make it easy on yourself, I suggest making m = 1, but it's really all up to you.