Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions,

express them in the ordered-pair form given in Example 6.

$\begin{array}{l}0.4x+1.2y=14\\ 12x-5y=10\end{array}$

Short answer

Hence, the solution of the system of equations $\begin{array}{l}0.4x+1.2y=14\\ 12x-5y=10\end{array}$is the ordered pair

Step-by-step solution

Step 1. Given information.

Given a system of equations$\begin{array}{l}0.4x+1.2y=14\\ 12x-5y=10\end{array}$

substitution method.

Step 2. Write down the concept.

Given equation,

$0.4x+1.2y=14$ …….(1)

$12x-5y=10$ …….(2)

Solving equation (1) for x,

$x=\frac{10}{4}\left(14-1.2y\right)$

Step 3. Determining the angle

We are substituting equation (3) in equation (2),

$12(35-3y)-5y=10$

$420-36y-5y=10$

Subtracting $420$ from both sides,

$-41y=-410$

Dividing both sides by -41

$y=10$

Now, substituting back value of y in equation (3)

$\begin{array}{l}x=35-3\left(10\right)\\ x=35-30\\ x=5\end{array}$