Which graph represents this system? 2x-5v=-5 y=-3x+1
1 answer:
Answer:
Please check the attached graph.
Step-by-step explanation:
The slope-intercept form of the line equation
where
- m is the slope
- b is the y-intercept
Given the system of equations
2x - 5y = -5 --- [Equation 1]
y = -3x + 1 --- [Equation 2]
converting the equation 1 in the slope-intercept form
2x - 5y = -5
5y = 2x+5
divide both sides by 5
y = 2/5x + 1
Thus, the y-intercept = 1
Now, please check the attached graph below.
The red line represents the equation 2x - 5y = -5
From the graph, it is clear that the red line has the y-intercept y = 1.
Now, considerng the equation 2
y = -3x + 1
comparing with the slope-intercept form of line equation
The y-intercept b = 1
Hence, the y-intercept of the line y = -3x + 1 is y = 1
The green line represents the equation y = -3x + 1
From the graph, it is clear that the green line has the y-intercept y = 1.
<u>Point of Intersection:</u>
It is clear from the graph:
- The red line represents the equation 2x - 5y = -5.
- The green line represents the equation y = -3x + 1.
As both lines meet or intersect at the point (0, 1).
Therefore, the point of intersection of both the lines is:
(x, y) = (0, 1)
As we know that the point of intersection of both the lines represents the solution to the system of equations.
Therefore, (0, 1) on the graph represents the solution to the system of equations.
The graph is attached below.
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La franja amarilla del rectángulo tiene un área de 30 centímetros cuadrados.
<h3>¿Cuál es el área de la franja amarilla del rectángulo?</h3>
En este problema tenemos un rectángulo formado por dos cuadrados que se traslapan uno al otro. La franja amarilla es el área en la que los cuadrados se traslapan. La anchura del rectángulo es descrita por la siguiente ecuación:
(10 - x) + 2 · x = 17
Donde x se mide en centímetros.
A continuación, despejamos x en la ecuación descrita:
10 + x = 17
x = 7
Ahora, el área de la franja amarilla se determina mediante la fórmula de area de un rectángulo:
A = b · h
Donde:
- b - Base del rectángulo, en centímetros.
- h - Altura del rectángulo, en centímetros.
- A - Área del rectángulo, en centímetros cuadrados.
A = (10 - 7) · 10
A = 3 · 10
A = 30
El área de la franja amarilla del rectángulo es igual a 30 centímetros cuadrados.
Para aprender más sobre áreas de rectángulos: brainly.com/question/23058403
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