Question
Graph using Des mos, then find the solution. y=(2)/(3)x+(1)/(3)y=x-1
Solution
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(271 Votos)
Anderson
Especialista · Tutor por 3 anos
Resposta
To solve the system of equations using the Desmos graphing tool, follow these steps:1. **Open Desmos**: Go to [Desmos Graphing Calculator](https://www.desmos.com/calculator).2. **Enter the first equation**: In the first input box, type `y = (2/3)x + (1/3)y` and press Enter.3. **Simplify the first equation**: To make it easier to graph, simplify the first equation. Combine like terms:
So, the first equation simplifies to
.4. **Enter the second equation**: In the second input box, type `y = x - 1` and press Enter.5. **Find the intersection**: The solution to the system of equations is the point where the two lines intersect.6. **Verify the solution**: From the graph, you should see that the lines intersect at the point \((1, -1)\). This is the solution to the system of equations.To find the solution algebraically, solve the system of equations:
Substitute
into the second equation:
Combine like terms:
This simplifies to:
This is a contradiction, indicating that there is no solution to the system of equations. Therefore, the lines are parallel and do not intersect.In conclusion, the system of equations has no solution because the lines are parallel.