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3 years ago

solve this system of linear equations. separate the x- and y- values with a comma. 6x +5y=-19 12x-8y=52

Mathematics

1 answer:

Ymorist [56]3 years ago

8 0

ANSWER

The solution is

(x,y)=(1,-5)

EXPLANATION

The equations are:

1st equation: 6x +5y=-19

2nd equation: 12x-8y=52

Multiply the first equation by 2:

3rd equation: 12x +10y=-38

Subtracy the 2nd equation from the 3rd equations.

12x-12x+10y--8y=-38-52

18y=-90

Divide both sides by 18.

y=-5

Put y=-5 into any of the equations and solve for x.

Preferably, the first equation will do.

6x +5(-5)=-19

6x -25=-19

6x=25-19

6x=6

x=1

The solution is

(x,y)=(1,-5)

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3 years ago

In a system of linear equations in two variables, if the graphs of the equations are the same, the equations are (blank) equat

makkiz [27]

Answer:

Please check the explanation.

Step-by-step explanation:

We know that when a consistent system has infinite solutions, then the graphs of the equations are exactly the same. In other words, these equations are called dependent equations.

All points of dependent equations share the same slope and same y-intercept.

For example,

6x-2y = 18

9x-3y=27

represent the dependent equations.

Writing both equations in slope-intercept form

y=mx+c

where m is the slope and c is the y-intercept

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y = 3x - 9

Thus, the slope = 3 and y-intercept = b = -9

now

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Therefore, both equations have the same slope and y-intercept. Their graphs are the same. Hence, they are called dependent equations.

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3 years ago

A line with a slope of -2 passes through the points (0,d) and (-8,9). What is the value of d?

Verizon [17]

The formula of a slope:

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

We have m = -2 and the points (0, d) and (-8, 9). Substitute:

$\dfrac{9-d}{-8-0}=-2\\\\\dfrac{9-d}{-8}=-2\qquad\text{multiply both sides by (-8)}\\\\9-d=16\qquad\text{subtract 9 from both sides}\\\\-d=7\qquad\text{change the signs}\\\\\boxed{d=-7}$