Question

without solving determine the number of solutions to each of the following system of linear equation 2x+3y=3 3x+4y=5​

Answer 1

By analyzing the ratios of coefficients in the given system of linear equations, we can determine that the lines will intersect at one point, meaning the system has exactly one solution.

Step-by-step explanation:

To determine the number of solutions to the system of linear equations without solving them, we can compare their coefficients. The two equations given are:

• 2x + 3y = 3
• 3x + 4y = 5

For a system of linear equations, the following scenarios are possible:

• One solution if the lines intersect at one point (consistent and independent).
• No solution if the lines are parallel and never intersect (inconsistent).
• Infinitely many solutions if the lines are coincident (consistent and dependent).

To predict the number of solutions, we check if the ratios of the coefficients of x and y, and the constants are equal or not.

Ratios:

• For x: 2/3
• For y: 3/4
• For constants: 3/5

Since the ratios are not the same, the lines are not parallel and they will intersect at one point. Hence, this system has exactly one solution.