### All Algebra 1 Resources

## Example Questions

### Example Question #2418 : Algebra 1

Solve the following system of equation

**Possible Answers:**

Cannot be solved

**Correct answer:**

Start with the equation with the fewest variables, .

Solve for by dividing both sides of the equaion by 6:

Plug this value into the second equation to solve for :

Subtract 10 from both sides:

Divide by 9:

Plug these and values into the first equation to find :

Combine like terms:

Subtract 2:

Divide by -4:

Therefore the final solution is .

### Example Question #11 : How To Find The Solution For A System Of Equations

Two integers, and , sum to 16, but when is doubled, they sum to 34. Find and .

**Possible Answers:**

No solution

**Correct answer:**

and add up to 16:

When is doubled to , they sum to 34:

We have two equations and two unknowns, so we can find a solution to this system.

Solve for in the first equation:

Plug this into the second equation:

Solve for :

Use this value to find . We already have a very simple equation for , .

Therefore the answer is .

### Example Question #201 : Algebra

Solve for .

**Possible Answers:**

**Correct answer:**

For the second equation, solve for in terms of .

Plug this value of y into the first equation.

### Example Question #5 : Systems Of Equations

If

and

Solve for and .

**Possible Answers:**

None of the available answers

**Correct answer:**

rearranges to

and

, so

### Example Question #1 : Linear Systems With Two Variables

Solve for in the system of equations:

**Possible Answers:**

The system has no solution

**Correct answer:**

In the second equation, you can substitute for from the first.

Now, substitute 2 for in the first equation:

The solution is

### Example Question #3 : How To Find The Solution For A System Of Equations

Without drawing a graph of either equation, find the point where the two lines intersect.

Line 1 :

Line 2 :

**Possible Answers:**

**Correct answer:**

To find the point where these two lines intersect, set the equations equal to each other, such that is substituted with the side of the second equation. Solving this new equation for will give the -coordinate of the point of intersection.

Subtract from both sides.

Divide both sides by 2.

Now substitute into either equation to find the -coordinate of the point of intersection.

With both coordinates, we know the point of intersection is . One can plug in for and for in both equations to verify that this is correct.

### Example Question #4 : How To Find The Solution For A System Of Equations

What is the sum of and for the following system of equations?

**Possible Answers:**

**Correct answer:**

Add the equations together.

Put the terms together to see that .

Substitute this value into one of the original equaitons and solve for .

Now we know that , thus we can find the sum of and .

### Example Question #21 : How To Find The Solution For A System Of Equations

Two lines have equations of and . At what point do these lines intersect?

**Possible Answers:**

**Correct answer:**

We can solve this problem by setting up a simple system of equations. First, we want to change the equations so one variable can cancel out. Multiplying the first equation by 2 and the second equation by 3 gives us a new system of and . These equations add up to or . Plugging in 7 for in either of the original two equations shows us that is equal to 1 and the point is .

### Example Question #22 : How To Find The Solution For A System Of Equations

Does this system of equations have one solution, no solutions, or infinite solutions?

**Possible Answers:**

one solution:

one solution:

no solution

infinite solutions

**Correct answer:**

infinite solutions

This system has infinite solutions becasue the two equations are actually the exact same line. To discover this, put both equations in terms of y.

First, . Add y to both sides:

Now add 3 to both sides:

Now we can show that the second equation also represents the line

add 6 to both sides

divide both sides by 2

Since both equations are the same line, literally any point on one line will also be on the other - infinite solutions.

### Example Question #23 : How To Find The Solution For A System Of Equations

Find the solution for the system of equations.

and

**Possible Answers:**

and

and

and

and

and

**Correct answer:**

and

A system of equations can be solved by subsituting one variable for another. Since we know that , we can subsitute this into the other equation so . This expression can be solved to find that . Now that we know the value of it can be subsituted into either of the original equations to find .