# Substitution help

#### campvoorhees23146

How to do these problems:

Substitution
Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution of Infinitely many solutions

1. 2x + 5y= 38
x - 3y = -3

2. x - 4y = 27
3x + y = -23

3. 2x + 2y = 7
x - 2y = -1

4. 2.5 + y = -2
3x + 2y = 0

PLEASE HELP ME!!! I've BEEN TRYING TO DO THIS SINCE 5:00 and its 10:39!!!!! YOU DESERVE A COOKIE IF YOU ARE ABLE TO HELP ME!!!!

#### Anonymous1

How to do these problems:

Substitution
Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution of Infinitely many solutions

1. 2x + 5y= 38
x - 3y = -3
$$\displaystyle 2x + 5y= 38\to (1)$$
$$\displaystyle x - 3y = -3 \to (2)$$

$$\displaystyle (2)\implies x = -3+3y$$

Now, sub this $$\displaystyle x$$ into $$\displaystyle (1)$$

$$\displaystyle 2\left\{-3+3y\right\} + 5y= 38$$

$$\displaystyle \implies -6 + 11y = 38 \implies \fbox{y = 4}$$

Now, sub this back into either $$\displaystyle (1)$$ or $$\displaystyle (2)$$ to find out what $$\displaystyle x$$ is.

You try some...