Question

Find the coordinates of the point of intersection of the line with equation 3x + 4y = 10 and the line with equation 5x − 6y = 23

Show your working clearly.

Answer 1

Answer:

(8/3, -0.5)

Step by step explanation:

Because we need to find the coordinates of the point of intersection of the line with those two equations, we need to figure out x and y. In order to do this, we need to put these two equations into one.

The least common multiple of 5 and 3 is 15, so:
3*(5x-6y)=3*23
15x-18y=69 1⃣️

5*(3x+4y)=5*10
15x+20y=50 2⃣️

Now we use 1⃣️-2⃣️=15x-18y-15x-20y=69-50
-38y=19
y=-0.5

Then we can get x
3x+4y=10
3x-2=10
3x=8
x=8/3

Then, we get the coordinates (8/3, -0.5)

Hope this will help:)

Answer 2

Answer: (4,-1/2)

Explanation:

`\displaystyle\\\left \{ {{3x+4y=10\ \ \ \ \ (1)} \atop {5x-6y=23\ \ \ \ \ (2)}} \right.`

Multiply equation (1) by 6 and equation (2) by 4:

`\displaystyle\\\left \{ {{18x+24y=60\ \ \ \ \ (3)} \atop {20x-24y=92\ \ \ \ \ (4)}} \right. \\`

Let's sum up the equations\ (3) and (4):

`38x=152`

Divide both parts of the equation by 38:

`x=4`

Hence,

`3(4)+4y=10\\12+4y=10\\12+4y-12=10-12\\4y=-2`

Divide both parts of the equation by 4:

`\displaystyle\\y=-(1)/(2)\\\\Thus,\ (4,-(1)/(2))`