Question

Sylvie finds the solution to the system of equations by graphing y=2/3x+1 and y=-2/3x-1 which graph shows the solution to sylvies system of equations

Answer 1

y = 2/3x + 1
y = -2/3x - 1
----------------add
2y = 0
y = 0

0 = 2/3x + 1
-2/3x = 1
x = 1 * -3/2
x = -3/2

solution is : (-3/2,0)

Answer 2

Solution of the two equations is (-1.5,0)

Explanation:

We are given two equations in the question:

`y = \displaystyle(2)/(3)x + 1\\\\y = \displaystyle(-2)/(3)x - 1`

The attached image shows the solution for the two equation.

As seen from the graph the solution for the two equations is (-1.5,0)

Solving can be shown as:

`y = \displaystyle(2)/(3)x + 1\\\\y = \displaystyle(-2)/(3)x - 1\\\\\text{Adding the two equations}\\\\2y = \displaystyle(2)/(3)x + 1 + \displaystyle(-2)/(3)x - 1 = 0\\\\\Rightarrow y = 0\\\text{Putting value of y in one of the equations, we get}\\\\0 = \displaystyle(2)/(3)x + 1\\\\x = (-3)/(2) = -1.5`

Thus, solution of the two equations is (-1.5,0)