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4 years ago

Solve the system:2x-5y=73x-2y=-17

1 answer:

8 0

$\begin{cases}2x-5y=7 \ \ /*3 \\ 3x-2y=-17\ \ / *(-2) \end{cases}\\ \\\begin{cases}6x-15y=21 \\ -6x+4y= 34 \end{cases}\\+ \ ------- \\-11y=55 \ \ / :(-11)\\ \\y=-\frac{55}{11}$

$y=-5 \\ \\ 2x-5y=7\\ \\2x-5*(-5)=7\\ \\2x+25=7\\ \\2x=7-25$

$2x=-18\ \ /:2 \\ \\ x=-\frac{18}{2} \\ \\x=-9 \\ \\\begin{cases} x=-9 \\ y=-5 \end{cases}$

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Which line has the same slope as the lone passing through (-4,-1) and (-1,-7)

Julli [10]

Answer:

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Step-by-step explanation:

1) First, find the slope of the line passing through (-4, -1) and (-1, -7). Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the two points into the formula and solve:

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So, the slope is -2.

2) Now, identify the slopes of the lines in the options. We already know the slope of $y = -\frac{1}{2} x-7$ is $-\frac{1}{2}$ since it is in slope-intercept form. y = -2 must have a slope of 0 since it's horizontal, and all equations with the format of y = a number are horizontal.

To find the slope of $6x + 3y = 5$ , isolate y to put the equations into slope-intercept form ( $y = mx + b$ format), and whatever the coefficient of the x-term is will be the slope.

$6x + 3y = 5\\3y = -6x+5\\y = -2x + \frac{5}{3}$ .

So, the slope of the first option is -2. It matches the slope we calculated in the first step, so that must be the answer.

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Step-by-step explanation:

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4 years ago

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