(3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0, (3, -2) is not a solution to the system of equations -x - y = -5 and 3x - 4y = 17 and (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6

<h3>How to determine the whether or not (3, -2) is a solution to the following systems?</h3>

The systems of equations are given as:

1. x - 2y = 7 and 2x + 3y = 0

2. -x - y = -5 and 3x - 4y = 17

3. x + y = 1 and x - y = 6

Next, we substitute (3, -2) for (x, y) in the system of equations.

So, we have:

3 - 2 * -2 = 7 and 2 * 3 + 3 * -2 = 0

Evaluate

7 = 7 and 0 = 0

The above equation is true

Hence, (3, -2) is a solution to the system of equations x - 2y = 7 and 2x + 3y = 0

-3 + 2 = -5 and 3 * 3 + 4 * 2 = 17

Evaluate

- 1 = - 5 and 1 7 = 1 7

The above equation is false

Hence, (3, -2) is not a solution to the system of equations -x - y = -5 and 3x - 4y = 17

3 - 2 = 1 and 3 + 2 = 6

Evaluate

1 = 1 and 5 = 6

The above equation is false

Hence, (3, -2) is not a solution to the system of equations x + y = 1 and x - y = 6

Read more about system of equations at:

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8 0

2 years ago

Sketch the quadratic function f(x) = -2x2 + 4x + 6. Which key feature of the graph is not true?

sertanlavr [38]

Answer:

D is false

Step-by-step explanation:

f(x) = -2x2 + 4x + 6 should be written with a " ^ " to indicate exponentiation:

f(x) = -2x^2 + 4x + 6.

Because of the - sign, we know that the graph of this function opens down, so there is a maximum at the vertex. We can determine the x-value at the vertex by using the formula x = -b/(2a), which here is x = -4/(2*-2), or 1.

Evaluating f(x) = -2x^2 + 4x + 6 at x = 1, we get -2 + 4 + 6, or 8. So statement A is true: there's a max at (1, 8). This is also the vertex of the graph.

Let's now look at C and D. We evaluate f(x) at x = 3 and x - 2. If the output (y) value is 0, we know we have an x - intercept:

f(3) = -2(9) + 4(3) + 6 = 0. Yes, C is true, (3, 0) is an x-intercept.

f(-2) = -2(4) - 8 + 6 is not 0. Therefore D is false; (-2, 0) is not an x-intercept.

Look at B: Let x = 0 and find y: it's 6. Thus, (0, 6) is the y-intercept. B is true.

4 0

3 years ago

Gavin was thinking of a number. Gavin doubles it and adds 6.6 to get an answer of 9. Form an equation with

Debora [2.8K]

Answer:

(9-6.6)÷2=x

Step-by-step explanation:

Do it in reverse from 9 all the way to x.

7 0

2 years ago

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