Question

Without drawing the graphs, find the points of intersection of the lines: a 7x+4y=23 and 8x–10y=19

Answer 1

(3,0.5)

Explanation:

The given system has equations:

`7x + 4y = 23 \\ 8x - 10y = 19`

Let us multiply the second equation by 4 and the first equation by 10.

`70x + 40y = 230 \\ 32x - 40y = 76`

We add both new equations to get:

`102x = 306 \\ x = (306)/(102) = 3`

Put x=3 into the first equation and solve for y.

`7(3) + 4y = 23 \\ 21 + 4y = 23 \\ 4y = 23 - 21 \\ 4y = 2 \\ y = (1)/(2)`

The point of intersection is the solution to the system of equation which is (3,0.5)