Question

Find the solution of y=x+3 and y=2x+6

Answer 1

x = 3 and y = 0

Explanation:

To find the solution where you have two equations is called a System of Equations.

What you do is you notice there are two equations and the let both equations equal each other. We can do this because both equations start with a y. These "y" work like puzzles and you can connect the "x+3" and "2x + 6" together. Then solve for it. Here's what i mean,

y = x+3

y = 2x+6

Now connecting them,

x+3 = 2x+6

Subtract x from both sides

3 = x + 6

Subtract 6 from both sides,

x = -3

Now solve for y,

y = -3 + 3 = 0

So our solution is x = 3 and y = 0.

Answer 2

(x, y) = (-3, 0)

Explanation:

Substitution or elimination work well for solving this system of equations.

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Elimination

Subtract the first equation from the second.

(y) -(y) = (2x +6) -(x +3)

0 = x +3

-3 = x . . . . . . . subtract 3

y = (-3) +3 = 0 . . . . use the first equation to find y

(x, y) = (-3, 0)

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Substitution

Use the second equation to substitute for y in the first.

2x +6 = x +3

x = -3 . . . . . . . . . subtract x+6 from both sides

y = (-3) +3 = 0 . . . . find y using the first equation

(x, y) = (-3, 0)

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A graphing calculator answers these quickly.