# How do you solve the system of equations #3x + y = 23# and #4x - y = 19#?

##### 2 Answers

X=6, Y=5

#### Explanation:

Use simultaneous equations (multiplying both equations, and eliminating either x or y by adding or subtracting to find the value of one, then plugging the value back in to find the other value)

The lowest common multiple of 3 and 4 is 12

This is the result:

From here as x is the same, you can subtract the bottom equation from the top leaving you with y. After doing this the result is:

Then we can plug this value back into the equations, then we can solve to find x.

We have got

So therefore these values fit both equations and we are correct.

The point of intersection is

#### Explanation:

You can also use substitution. The resulting values for

Equation 1:

Equation 2:

Solve Equation 1 for

Subtract

Substitute

Simplify.

Add

Simplify.

Divide both sides by

Substitute

Simplify.

Subtract

The point of intersection is

Equation 1:

Equation 2:

graph{(y+3x-23)(-y+4x-19)=0 [-15.69, 16.34, -5.83, 10.19]}