How to find the solution for a system of equations - Algebra 1 (2024)

Correct answer:

Explanation:

Since the object in question is a cube, each of its sides must be the same length. Therefore, to get a volume of , each side must be equal to the cube root of , which is cm.

We can then set each expression equal to .

The first expression can be solved by either or , but the other two expressions make it evident that the solution is .

Correct answer:

Explanation:

The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply by to get .

Then, we can add to this equation to yield , so .

We can plug that value into either of the original equations; for example, .

So, as well.

Correct answer:

Explanation:

By solving one equation for , and replacing in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.

None of the other choices are correct.

Correct answer:

Explanation:

Multiply the bottom equation by 5, then add to the top equation:

None of the other choices are correct.

Correct answer:

Explanation:

Multiply the top equation by:

Now add:

None of the other choices are correct.

Correct answer:

Explanation:

Multiply the top equation by :

Now add:

Correct answer:

Explanation:

To solve this system of equations, use substitution. First, convert the second equation to isolate .

Then, substitute into the first equation for .

Combine terms and solve for .

Now that we know the value of , we can solve for using our previous substitution equation.

no solution

infinitely many solutions

Correct answer:

no solution

Explanation:

When we add the two equations, the and variables cancel leaving us with:

which means there is no solution for this system.

None of the other answers

Correct answer:

Explanation:

First, combine like terms to get . Then, subtract 12 and from both sides to separate the integers from the 's to get . Finally, divide both sides by 3 to get .

none of these

Correct answer:

Explanation:

We are given the following system of equations:

We are to find and . We can solve this through the substitution method. First, substitute the second equation into the first equation to get

Solve for by adding 4x to both sides

Add 5 to both sides

Divide by 7

So . Use this value to find using one of the equations from our given system of equations. I think I'll use the first equation (can also use the second equation).

So the two linear functions intersect at