# Solving Equations by Graphing System of Equations

## Tenisha's Equation Solution

Tenisha solved the equation below by graphing a system of equations:

Which point approximates the solution for Tenisha’s system of equations?

- (0.9, 0.8)
- (1.0, 1.4)
- (2.3, 1.1)
- (2.7, 13.3)

Mathematics, log3 5x = log5 (2x + 8) implies log3 5x = 2log5 . x + 8log5

log3 5x - 2log5 . x = 8log5 and (5log3 - 2log5)x = 8log5

Finally, x = 8log5 / (5log3 - 2log5) = a

Let y = log5 (2x + 8), so y(a) = log5 (2a + 8)

The point approximating the solution is P(a, y(a)) or P(8log5 / (5log3 - 2log5), log5[2 (8log5 / (5log3 - 2log5)) + 8])

Therefore, by graphing a system of equations, the points that approximate the solution for Tenisha’s system of equations are points (1.0, 1.4).

What point approximates the solution for Tenisha's system of equations?(1.0, 1.4) is the correct answer :)