Solving A System Of Equations Using The Method Of Substitution

What is the solution to the following system of equations?y = -3x+6y = 12x-24

( 2, 0 )

To solve this system of equations, we need to find the values of x and y that make both equations true simultaneously. One way to do this is to use the method of substitution, which involves isolating one variable in one of the equations and then substituting its expression into the other equation.

Starting with the first equation, we can isolate y by subtracting -3x from both sides:

y = -3x + 6

Now we can substitute this expression for y into the second equation and solve for x:

y = 12x – 24

-3x + 6 = 12x – 24

Adding 3x to both sides, we get:

6 = 15x – 24

Adding 24 to both sides:

30 = 15x

Dividing by 15:

x = 2

Now that we know x = 2, we can substitute it back into either equation to find y. Let’s use the first equation:

y = -3x + 6

y = -3(2) + 6

y = 0

So the solution to the system of equations is (2,0). That is, the values of x and y that satisfy both equations are x = 2 and y = 0.

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