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

Answer 1

Answer: (4,-1/2)

Step-by-step 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:

$\displaystyle\\y=-\frac{1}{2}\\\\Thus,\ (4,-\frac{1}{2})$

Answer 2

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:)