Answer to Question #103819 in Algebra for tyler

Question

Create a list (table) of three solutions for this equation: 3x + 2y = -18. Provide work to support the solutions and write the solutions as ordered pairs.

Answer 1

Given equation has two variable x and y. To find any number of solution (not just three) we can make table of values where we assign some random value to one variable and solve the equation for other variable. It will give order pair (x,y) which will satisfy the equation and hence it will be a solution for given equation.

Here we are free to choose any value of x or y but it is sometimes convenient to use x = 0 or y=0 and solve equation for other variable (choosing x=0 or y=0 makes the equation easy to solve)

Given equation

$3x + 2y = -18$

Let x = 0

$3(0) + 2y = -18$

$0 + 2y = -18$

$2y = -18$

$y=-\frac{18}2$

$y= -9$

Hence $(0 , -9)$ is one of the solution.

Now let y=0

3$x+2(0)=-18$

$3x+0=-18$

$3x=-18$

$x=-\frac{18}3$

$x=-6$

Hence $(-6, 0)$ is another solution of given equation.

Now for third solution, let x = 2

$3(2)+2y=-18$

$6+2y=-18$

$2y=-18-6$

$2y=-24$

$y=-\frac{24}2$

$y=-12$

Hence $(2, -12)$ will be third solution.

Answer: (0, -9) , (-6, 0) and (2, -12)