What are the solutions to the system of equations?

Question

y=x²- 5x+6

y=-4x+6

Answer 1

Hi Ari!

To solve these equations, the first step you should take is setting the equations equal to each other. Since they both equal y, the equations can be equal.

So now, set up your equation as x² - 5x + 6 = -4x + 6

Now, combine like terms. So you can begin by adding 4x to -5x, making the equation now x² - x + 6 = 6. You can now subtract 6 from both sides, so your equation is now x² - x.

You can factor out an x, since there is an x in both terms, so you are left with x(x-1). You can now set both parts of this equation equal to 0, separately.

So, pull out the x and set it equal to 0. x=0. 0 is your first solution.

Now, set x-1 = 0. Add 1 to both sides, and your second solution is 1. Your solutions are x = 0 and x = 1

To solve for y, simply plug both x's back into either equation (since they are both equal to y, it doesn't matter which one you choose) and do this for both x's.

y = -4x +6 ----> y = -4(0) +6. When you solve, -4(0) = 0, so you are only left with y=6. Your first solution set is (0,6)

To solve for the next solution set, simply plug 1 into the same equation as x. so, y = -4(1) +6. -4(1) = -4, and if you add 6, you are then left with y = 2. So your second solution set is (1,2)

Answer 2

y = x^2 - 5x + 6

y = -4x + 6

we can equate those two equations since they are both equal to y

x^2 - 5x + 6 = -4x + 6

x^2 - 5x +4x +6 = -4x + 4x + 6

x^2 -x + 6 = 6

x^2 -x +6 - 6 = 6 -6

x^2 - x = 0

x(x-1) = 0

x = 0

x-1 = 0 --> x = 1

x = 0 or 1

plug x = 0 and 1 into second equation (since it is simpler to deal with):

y = -4(0) + 6 = 6

y = -4(1) + 6 = 2

solutions are (0,6) and (1,2), which you can plug into both equations to verify