Solve {l}{3a+a=-a}{2a+7/b-a=5}

$$\left\{ \begin{array} { l } { 3 a + a = - a } \\ { \frac { 2 a + 7 } { b - a } = 5 } \end{array} \right.$$

Solve for a, b

$$a=0$$

$$b = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

Solution Steps

Consider the first equation. Combine 3a and a to get 4a.

$$4a=-a$$

Add a to both sides.

$$4a+a=0$$

Combine 4a and a to get 5a.

$$5a=0$$

Divide both sides by 5. Zero divided by any non-zero number gives zero.

$$a=0$$

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

$$\frac{2\times 0+7}{b-0}=5$$

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.

$$2\times 0+7=5b$$

Multiply 2 and 0 to get 0.

$$0+7=5b$$

Add 0 and 7 to get 7.

$$7=5b$$

Swap sides so that all variable terms are on the left hand side.

$$5b=7$$

Divide both sides by 5.

$$b=\frac{7}{5}$$

The system is now solved.

$$a=0 b=\frac{7}{5}$$