what i need answered

Question

 Solve the system: x = 5y - 1 and x + 2y = 13 Write your answer as a coordinate point

Answer 1

Let's use a substitution approach here.

You have an equation with x by itself on the left-hand side, and you have an equation with x and y on the left-hand side. Look at x = 5y - 1. This can be plugged in to the other equation because x is by itself, and so you know exactly what x is equal to! There's no riddle as to the identity of x, because x is clearly identified here! Let me show you here:

I know that x = 5y - 1.

Plug this info into the other equation.

The other equation: x + 2y = 13

(5y - 1) + 2y = 13

Since we replaced x, we now have an expression with only y's. The fewer variables, the better! Now simplify this and solve for y.

(5y - 1) + 2y = 13

7y - 1 = 13 (by combining like terms, the y-terms)

7y = 14 (by adding 1 on both sides)

y = 2 (by dividing 7 on both sides)

So since I have the y-coordinate of my answer, my final answer looks something like this: ( x , 2 ).

But what is x, you ask? Well, let's find it!

You can go to either of the original equations to find what x is. I pick x = 5y - 1. Use your new-found knowledge about y to find the answer!

x = 5y - 1

x = 5(2) - 1

x = 10 - 1

x = 9

So since I have the x-coordinate of my answer, my final answer looks something like this: ( 9 , y ).

We have both parts now!

(9, 2) is the solution to this system of equations.

Answer 2

Use substitution

x = 5y - 1

x + 2y = 13

5y - 1 + 2y = 13

Can you solve for y and answer?