Solve (x)=5x+1,g(x)=6-4x.

$$( x ) = 5 x + 1 , g ( x ) = 6 - 4 x .$$

Solve for x, g

$$x=-\frac{1}{4}=-0.25$$

$$g=-28$$

Solution Steps

Consider the first equation. Subtract 5x from both sides.

$$x-5x=1$$

Combine x and -5x to get -4x.

$$-4x=1$$

Divide both sides by -4.

$$x=-\frac{1}{4}$$

Consider the second equation. Insert the known values of variables into the equation.

$$g\left(-\frac{1}{4}\right)=6-4\left(-\frac{1}{4}\right)$$

Multiply -4 and -\frac{1}{4} to get 1.

$$g\left(-\frac{1}{4}\right)=6+1$$

Add 6 and 1 to get 7.

$$g\left(-\frac{1}{4}\right)=7$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$g=7\left(-4\right)$$

Multiply 7 and -4 to get -28.

$$g=-28$$

The system is now solved.

$$x=-\frac{1}{4} g=-28$$