Find the point of intersection between two lines y=2x+4 and 2y+3x=1:

Initially drawing a diagram of the two lines helps to establish whether values should be positive or negative and gives a rough approximation of where the answer may be:

By doing this we see the point of intersection is approximately a x value between 0 and -2, and the y co-ordinate is between 0 and 4

Today we will solve this problem by substitution

We call the equation y=2x+4 equation 1

And 2y+3x=1 equation 2

Substituting equation 1 into equation 2 we get:

2(2x+4) + 3x=1

This simplifies to: 4x+8+3x=1

Therefore: 7x=-7

X=-1

Now we have our x coordinate we can sub it back into either equation to get the y coordinate eg. In equation 1

Y=2(-1) + 4

Y=2

We can check our result in equation 2:

2(2) + 3(-1) =1