Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite. 3x + 2y = 6 x - y = 2
{}
1 solution
infinite

Answer 1

The solution set for the system of equations contains one point

The system of the equations has one solution

Step-by-step explanation:

The system of the linear equations has:

• 1 solution if the 2 lines that represent the equations intersect each other in one point
• No solution "{}" if the 2 lines that represent the equations are parallel
• Infinite solutions if the 2 lines that represent the equations are coincide (same line)

→ Intersected lines have different slopes

→ Parallel lines have same slopes and different y-intercepts

→ Coincide lines have same slopes and same y-intercepts

Let us put each equation in the form y = m x + c, where m is the slope

and c is the y-intercept

∵ 3x + 2y = 6

- Subtract 3 x from each side

∴ 2y = 6 - 3 x

- Divide both sides by 2

∴ y = 3 - 1.5 x

∴ y = -1.5 x + 3

∵ y = m x + c

∴ m = -1.5 and c = 3

∵ x - y = 2

- Subtract x from both sides

∴ -y = 2 - x

- Divide both sides by -1

∴ y = -2 + x

∴ y = x - 2

∵ y = m x + c

∴ m = 1 and c = -2

∵ The two equations have different slopes

∴ The two line are intersected in a point

∴ The system of the equations has one solution

The solution set for the system of equations contains one point

The system of the equations has one solution

Learn more:

You can learn more about the system of equations in brainly.com/question/13168205

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