Step-by-step explanation:
Given the following system of equations
y = 3/2 x + 2
y = -2x - 5
Step 1: we need to find the x - intercept and y - intercept of each equation
To find the y - intercept of the first equation, make x = 0
Given ; y = 3/2x + 2
To find y, make x = 0
y = 3/2(0) + 2
y = 0 + 2
y = 2
When x = 0, y = 2 ----- (0, 2)
To find x , Let y = 0
y = 3/2x + 2
0 = 3/2x + 2
Collect the like terms
0 - 2 = 3/2x
-2 = 3/2x
Cross multiply
-2 * 2 = 3x
3x = -4
x = -4/3
When y = 0, x = -4/3-------------------- (-4/3, 0)
For the second equation
We are given the below equation
y = -2x - 5
To find y, make x = 0
y = -2(0) - 5
y = 0 - 5
y = -5
When x = 0, y = -5 ---------------- (0, -5)
Find x, when y = 0
0 = -2x - 5
Collect the like terms
0 + 5 = -2x
5 = -2x
Divide both sides by -2
-2x/-2 = 5/-2
x = -5/2
When x = -5/2, y =0 ------------------------ (-5/2, 0)
Step 2: Graph the equation