Question

Solve the following system of equations by substitution: 5x + 2y = 14 y = x – 7 Question 11 options: (–3, 4) (2, –5) (4, –3) (–5, 2)

Answer 1

To solve this system using substitution, start by writing them next to each other. You can see that the y value is already isolated with its own value (x - 7).

So, since y equals that expression, you can substitute it into your first given equation for the y.
This leaves you with:
5x + 2(x - 7) = 14

Then, use the distributive property to simplify your equation.
This ends up with:
5x + 2x - 14 = 14

Combine like terms by adding the coefficients in front of your x’s.
This results in:
7x - 14 = 14

Begin to isolate your variable by adding 14 to both sides.
This leaves you with:
7x = 28

Divide both sides by 7 to find the value of x in your solution.
This results in:
X = 4
So you know that the x value in your final ordered pair will be a 4.
At his point you could eliminate answer options and find the correct one, however to find your y value:

Substitute in your x to the simplest equation you were given in the system at the beginning.
This would be y = x - 7
Plugging in the value leaves you with:
y = 4 - 7
Subtract to find your final answer.
4-7= -3

So your y value is -3.

This makes your final ordered pair option C. (4, -3)