Determine where the two lines y = 3x – 5 and 2x – 4y = 10 intersect

Answer 1

y = 3x - 5

2x - 4y = 10

2x = 10 + 4y

2x - 10 = 4y

(2x - 10)/4 = y

both equations are now solved for y.

Let y = y

3x - 5 = (2x - 10)/4

12x - 20 = 2x - 10

10x = 10

x = 1

By substitution, y = -2

This is where the lines cross and it is a solution for each equation.

Answer 2

The point where the two equations intersect, means the place where they have the same x and y value.

Thus, we need to substitute one of the equations into the other.

Let's substitute the first equation into the second:

=> 2x - 4(3x - 5) = 10 (distributive property, be careful to factor the negatives appropriately!)

=> 2x - 12x + 20 = 10 (subtract 10 from each side and combine the x's)

=> -10x +10 = 0 (add 10x to each side)

=> 10x = 10 (divide each side by 10)

=> x = 1

Now that we've found x, we need to plug it back in (to either equation to solve for y)

I think it's easiest/fastest to substitute into the first equation.

=> y = 3(1) - 5

=> y = -2

Hence, the coordinate of intersection for these two lines is at (-1, 2).