how to solve 3x=-18+4y and 16y=58+5x using elimination

Question

work all the steps and give the full answer to the problem please

Answer 1

When solving a system of linear equations, the first thing you want to do is bring all the variables to one side.

Hence,

3x = -18 + 4y becomes 3x - 4y = -18

16y = 58 + 5x becomes -5x + 16y = 58

Now, we will eliminate one of the variables. Choose the variable that "seems easier" to eliminate.

In this case, I will choose y since 16 is a multiple of -4.

So,

3x - 4y = -18 (multiply by 4)

-5x + 16y = 58

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12x - 16y = -72

-5x + 16y = 58

Now, add the 2 equations

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7x = -14

x = -2

Next, we find the y value using the x value we just found by plugging it into ANY of the 2 equations.

I'll choose the first equation.

So,

3(-2) - 4y = -18

-6 - 4y = -18

-4y = -12

y = 3

Therefore, x = -2 and y = 3 OR (-2,3).

*Please feel free to ask me any question for clarification.

Answer 2

3x=-18+4y and 16y=58+5x using elimination

First , write them in a standard form:

3x=-18+4y~~~~~~~~~~~ 4y=3x+18

16y=58+5x ~~~~~~~~~~ 16y=5x+58

when you put those two equation, you have system equation:

4y=3x+18

16y=5x+58

Second, "using elimination", just means get rid of one variable.

let's multiply by 4 for the first equation, you get:

16y=12x+72

Now, compare two equations. Both are 16y= something, therefore, 12x+72=5x+58

when you solve, get x=-2.

Substitute x=-2 to the one of the original equation, pick 3x=-18+4y. you get y=3.

Note: always try to substitute one answer to the original equation to get other answer.

Make sure plug x=-2 and y=3 to both equations and check answers.

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Answer 3

1) 3x - 4y = -18

2) -5x + 16y = 58

Multiply equation 1) by 4 so that the "y"s have opposite integers as coefficients.

After multiplying by 4-> 1) 12x -16y = -72

2) -5x + 16y = 58

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Add the equations: 3) 7x = -14 => x = -2 (you are allowed to do this because equals added to equals are equal)

Substitute -2 for x in any of these equations ans solve for y.

1) 3(-2) -4y = -18

-6 - 4y = -18

-4y = -12

y = 3

Verify (if you want) that x = -2, y = 3 satisfies both equations.