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).

(1.0, 1.4) is the correct answer :)