How can I substitute this equation using a substitution method for b) y = 2x + 5
y = -3x - 10

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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.

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step-by-step explanation:

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