Question

Solve the following systems of equations algebraically:
$\left \{ {{y=\frac{1}{2}*2^x } \atop {y=5x+2}} \right.$

Answer 1

The value of x in the system of equation is 6

How to solve the system of equations?

The system of equations is given as:

y = 1/2 * 2^x

y = 5x + 2

Substitute y = 1/2 * 2^x in y = 5x + 2

1/2 * 2^x = 5x + 2

Multiply through by 2

2^x = 10x + 4

Next, we use the trial by error.

Set x = 6

This gives

2^6 = 10 * 6 + 4

Evaluate the product and the exponent

64 = 60 + 4

Evaluate the sum

64 = 64

Hence, the value of x in the system of equation is 6

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