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2 years ago

Help, please! ASAP!!

Mathematics

1 answer:

In-s [12.5K]2 years ago

5 0

Answer:

a) one solution

b) no solution

Step-by-step explanation:

Systems of equations can be described as having one solution, no solution or infinite solutions:

One solution: 'x' and 'y' are equal to only one value

No solution: 'x' and 'y' can not be solved with the given equations

Infinite solutions: values for 'x' and 'y' include all real numbers

In order to evaluate the systems, putting them in the same format is your first step:

a) - y = -5x - 6 or y - 5x = 6

y - 5x = -6

Since both equations have the same expression 'y - 5x', but there are equal to opposite values, this system would have no solution, as this would not be possible to calculate.

b) y + 3x = -1

y = 3x -1 or y - 3x = -1

Solving for 'y' by adding the equations and eliminating 'x', gives us:

2y = -2 or y = -1

Using y = -1 to plug back into an equation and solve for 'x': -1 + 3x = -1 or x = 0. Since 'x' and 'y' can be solved for a value, the system has just one solution.

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Which equation does the graph of the systems of equations solve?

mihalych1998 [28]

Answer:

$\text{B. }\frac{1}{3}x-3=-x+1$

Step-by-step explanation:

Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to $(x_1,y_1)$ and $(x_2, y_2)$ (doesn't matter which you assign) and use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let:

$(x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)$

The slope is equal to:

$m=\frac{0-1}{1-0}=\frac{-1}{1}=-1$

Therefore, the slope of this line is -1. In slope-intercept form $y=mx+b$ , $m$ represents slope, so one of the lines must have a term with $-x$ in it, which eliminates answer choices A and D.

For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:

$(x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)$

Using the slope formula:

$m=\frac{-2-(-3)}{3-0}=\frac{1}{3}$

Thus, the slope of the line is 1/3 and the other line must have a term with $\frac{1}{3}x$ in it, eliminating answer choice C and leaving the answer $\boxed{\text{B. }\frac{1}{3}x-3=-x+1}$

*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into $y=mx+b$

7 0

3 years ago

Help, please! ASAP!!​

Help, please! ASAP!!