What is the solution for the system of equations: 4/5x=y-5, (3x-4)/2=y?

Oct 26, 2016

$x = 10 \mathmr{and} y = 13$

Explanation:

In addition to these equation being a system which need to be solved together, you should realise that they represent the equations of straight line graphs.

By solving them, you also finding the point of intersection of the two lines. If both equations are in the form $y = \ldots .$, then we can equate the y's

$y = \frac{4}{5} x + 5 \mathmr{and} y = \frac{3 x - 4}{2}$

Since $y = y$ it follows that the other sides are also equal:

$\frac{4}{5} x + 5 = \frac{3 x - 4}{2} \text{ } \leftarrow \times 10$

$\frac{{\cancel{10}}^{2} \times 4 x}{\cancel{5}} + 10 \times 5 = \frac{{\cancel{10}}^{5} \times \left(3 x - 4\right)}{\cancel{2}}$

$8 x + 50 = 15 x - 20$

$50 + 20 = 15 x - 8 x$

$70 = 7 x$

$x = 10 \text{ } \leftarrow$ this is the x value

$y = \frac{4}{5} \left(10\right) + 5 = 13$

Check in other equation: $y = \frac{3 \times 10 - 4}{2} = \frac{26}{2} = 13$

The point of intersection between the 2 lines would be $\left(10 , 13\right)$