What should be done to these equations in order to solve a system of equations by elimination?

Mathematics

1 answer:

morpeh [17]3 years ago

7 0

Answer

You can multiply the first equation by 4 and the second equation by 3.

You can multiply the first equation by 4/3.

You can multiply the first equation by 3.

Explanation

When solving a system of equations by elimination, you want to add or subtract the equations to "get rid" of a variable.

To do that, one of the variables in both equations have to have the same coefficient.

The first answer possible gives x the coefficient of 12 for both equations. You would get 12x+4y=52 and 12x-9y=39. You could subtract those equations to get 13y=13.

The second way gives x the coefficient of 4. You would multiply the first equation by 4/3 to get 4x+4/3y=52/3. You can subtract to get one variable, and then solve from there. Although, multiplying for 4/3 is annoying, so it's not suggested.

You can also "get rid" the the y. Multiply the first equation by 3 to get 9x+3y=39. You can add these equations. When you add 9x+3y=39 and 4x-3y=13 you get 13x=52.

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Solve for all possible values of x. square root of the quantity x plus 6 end quantity plus 5 equals 17

Georgia [21]

Answer:

$x=138$

Step-by-step explanation:

So we have the equation:

$\sqrt{x+6}+5=17$

First, let's determine the domain restrictions. Recall that the radicand cannot be negative. In other words, it must be greater than or positive than 0. Thus:

$x+6\geq 0$

Subtract 6 from both sides:

$x\geq -6$

What this means is that our solutions must be greater than or equal to -6. If not, we ignore them.

So, let's subtract 5 from both sides from the original equation:

$\sqrt{x+6}=12$

Square both sides:

$x+6=144$

Subtract 6 from both sides:

$x=138$

138 is greater than -6, so 138 is a solution and is the only solution.

And we're done!

8 0

3 years ago

Yellowstone National Park is a popular field trip destination. This year the senior class at High School A and the senior class

Rina8888 [55]

Each van carries 13 students and each bus carries 25 students.

<h3><u>Distribution</u></h3>

Given that the senior class at High School A and the senior class at High School B both planned trips to Yellowstone, and the senior class at High School A rented and filled 5 vans and 2 buses with 115 students, while High School B rented and filled 1 van and 6 buses with 163 students, and each van carried the same number of students and each bus carried the same number of students, to determine the number of students in each van and in each bus, the following calculation must be made: