Solve the following system of equations: 4x+5y=23 -3x-7y=-14

Mathematics

1 answer:

Korvikt [17]3 years ago

5 0

Basically you're solving for both variables here.
I prefer elimination method so that is what I used.
I started off by multiplying each equation in order to get one of the variables at the same value so it would be possible to cancel it out.
Multiplying the first equation by 3 gave me,
12x + 15y = 69
Then I multiplied the second equation by 4,
-12x + 28y = -56
As you can see, it's not possible to cancel out the x variable.
12x + 15y = 69
+(-12x + 28y = -56)
_____________
13y = 13
Then just solve for y which gives you -1.
After you have one variable solved simply insert it into one of the original equations to find the other variable.
4x + 5(-1) = 23
4x - 5 = 23
4x = 28
x = 7.
And there you have it! Hope this helped!

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Plug these values into the slope formula:

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Therefore, the slope of f(x), m = 8.

The y-intercept of the function, f(x) is given by (0, -1), as it is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0.

The equation of the linear function, f(x) is:
f(x) = 8x - 1.

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The function, g(x) = 3x - 2 has a slope of 3, and y-intercept of -2.

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Attached is a screenshot of the graph of both lines, including their y-intercepts. The blue line is g(x) = 3x - 2, and the red line is f(x) = 8x - 1.

Please mark my answers as the Brainliest if you find this helpful :)