# How do you solve the following linear system # 3 x-2y=4 , x+4y=3#?

##### 2 Answers

#### Explanation:

1) Rearrange your equations to make them easier to use. The easiest way to do this is to isolate ONE variable that has the coefficient of 1.

# 3x - 2y = 4 #

# x = -4y + 3 #

2) Since you now know what the x variable is in terms of y, you can go ahead and substitute it into the first equation.

# 3 (-4y + 3) - 2y = 4 #

3) Simplify

# 3 (-4y + 3) - 2y = 4 #

# -12y + 9 - 2y = 4 #

# -14y + 9 = 4 #

# -14y = -5 #

# y = 5/14 #

4) Substitute the solution you just got to get the second variable.

# x + 4y = 3 #

# x + 4 (5/14) = 3 #

# x + 10/7 = 3 #

# x = 11/7 #

#### Explanation:

Using the second equation, derive a value for

Subtract

In the first equation, substitute

Open the brackets and simplify. The product of a positive and a negative is a negative.

Subtract

Divide both sides by

In the second equation, substitute

Open the brackets and simplify.

Subtract