Solve the System of Equations: -2x + 3y = 14 and -4x + 6y = 28

Question

Choose the correct answer for the following exercise:

$\begin{cases} -2x+3y=14 \\ -4x+6y=28 \end{cases}$

00:00 Solve the system of equations

00:06 Multiply by 2 so we can isolate Y by subtraction

00:13 Now this is the system of equations

00:23 Subtract between the equations

00:32 Group like terms

00:40 According to this expression, X and Y are correct for any value

00:56 And this is the solution to the question

To solve this system of equations, follow these steps:

Step 1: Simplify the second equation:
The second equation is $-4x + 6y = 28$ . By dividing every term by 2, we get:
$-2x + 3y = 14$ .
Step 2: Compare the simplified second equation to the first equation:
Both equations are now $-2x + 3y = 14$ .

Since both equations are identical after simplification, this indicates that the system represents the same line.

Therefore, the system has infinite solutions because any point that satisfies one equation will satisfy the other.

Thus, the correct answer is Infinite solutions.

Infinite solutions