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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