Answer: (x, y) = (-3, -1)
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Step-by-step explanation:
y = 2x+5 .... start with the first equation
-3x-10 = 2x+5 .... replace y with -3x-10 since y = -3x-10
The term "substitution" is the same as "replacement". Think of how the substitute teacher is a temporary replacement for your actual teacher.
Now we solve for x. Get all the x terms to one side and the non x terms to the other side
-3x-10 = 2x+5
-10-5 = 2x+3x
-15 = 5x
5x = -15
Next we divide both sides by 5 to isolate x
5x/5 = -15/5
x = -3
Now that we have the value of x, we can use this to find y. Pick any of the two equations to plug in this x value
y = 2x+5 = 2*(-3)+5 = -6+5 = -1
or
y = -3x-10 = -3(-3)-10 = 9-10 = -1
Either way, x = -3 leads to y = -1.
The fact we get the same y value helps us confirm we have the correct x value.
The solution to the system is (x,y) = (-3, -1)
This linear system is considered consistent and independent.
If you graph y = 2x+5 and y = -3x-10, you will find that the two lines intersect at (-3, -1) as the diagram shows below.