### All SAT Math Resources

## Example Questions

### Example Question #271 : Algebra

Solve the following system of equations:

**Possible Answers:**

**Correct answer:**

We can solve this system of equations by elimination.

By adding the second equation to the first, we get or .

Substitute y=-4 into either equation and solve for x.

Simplify and solve for x to get .

Therefore, the solution to this system of equations as an ordered pair is (7, -4).

### Example Question #53 : Systems Of Equations

You've gone to a bakery to get some fresh baked goods. You notice that the person in front of you in the checkout line buys 3 scones and 4 donuts for $10. You get 3 scones and 5 donuts for $12. How much do donuts cost at the bakery?

**Possible Answers:**

**Correct answer:**

We can express this problem as a system of equations where s represents scones and d represents donuts.

We can solve this system of equations by elimination as follows:

Subtracting the second equation from the first yields or .

Therefore, donuts cost $2.

### Example Question #51 : How To Find The Solution For A System Of Equations

Louise and Jon are running for Student Body President. At their school, a total of 250 students vote in the election. Louise receives 50 more votes than Jon. If everyone votes only once, what percentage of the vote did Louise receive?

**Possible Answers:**

**Correct answer:**

We can express the given information as a system of equations. Let L represent the votes cast for Lisa, and let J represent the votes cast for Jon.

The total votes cast in the election can be written as

Since Lisa received 50 more votes than Jon, we can write

We can solve this system of equations by substitution.

Let's rewrite the second equation in terms of J.

.

Now, we can substitute into .

This gives us

We can simplify this to get .

To calculate the percentage of the votes that were cast for Lisa, we take her 150 votes and divide them by the total number of votes cast in the election. Then, we multiply that by 100%.

0.6 x 100% = 60%

### Example Question #272 : Algebra

The sum of four consecutive even integers is , but their product is . What is the least of those integers?

**Possible Answers:**

**Correct answer:**

Any time the product of consecutive numbers is , must be a one of those consecutive numbers, because if it is not, the product will be non-zero. This leaves us with four possibilities, depending on where is placed in the sequence.

As we can see, , , and are our numbers in question, meaning is our answer as the lowest number.

Note that it is possible to use algebra and set up a system of equations, but it's more time-consuming, which could hinder more than help in a standardized test setting.

### Example Question #271 : Equations / Inequalities

How many solutions are there to the following system of equations?

**Possible Answers:**

There are no solutions.

There are 2 solutions.

There are 3 solutions.

There is 1 single solution.

There are an infinite number of solutions.

**Correct answer:**

There are an infinite number of solutions.

If we use elimination to solve this system of equations, we can add the two equations together. This results in 0=0.

When elimination results in 0=0, that means that the two equations represent the same line. Therefore, there are an infinite number of solutions.

### Example Question #272 : Algebra

Solve the system of equations:

**Possible Answers:**

None of the given answers.

**Correct answer:**

We can solve this system of equations by elimination since the 2 given y-values have the same coefficient. Let's subtract the second equation from the first.

This gives us or .

Substitute this x-value into either equation and solve for y. Let's use the first equation like so:

The solution is .

### Example Question #61 : Systems Of Equations

Solve the system of equations given below.

**Possible Answers:**

**Correct answer:**

We can solve this problem by elimination.

Subtract the second equation from the first to eliminate the x values, like so:

This yields

Now, substitute into either equation and solve for x. In either equation, we find that .

Therefore, the solution to this system of equations is .

### Example Question #61 : Systems Of Equations

At the cafe, Jalynn buys five donuts and a cup of coffee for . Giovanni buys five donuts and two cups of coffee for . How much does each cup of coffee cost?

**Possible Answers:**

**Correct answer:**

To solve this problem, we can set up a system of equations.

Let represent the cost of donuts, and let represent the cost of a cup of coffee.

We can write Giovanni and Jalynn's purchases as equations like this:

To solve this system of equations, we can use elimination by subtracting the second equation from the first, like so:

Our terms drop out, leaving us with

Therefore, each cup of coffee costs .

### Example Question #62 : Systems Of Equations

Solve the system of equations:

**Possible Answers:**

**Correct answer:**

Because the coefficients of the values are the same, we can solve this problem by elimination. Subtract the second equation from the first:

This knocks out our value and gives us , or .

Then, substitute this value into either of the equations to solve for . Let's use the second equation:

Therefore, the solution is

### Example Question #61 : Systems Of Equations

Solve the system of equations:

**Possible Answers:**

**Correct answer:**

Since none of our coefficients are the same, we cannot solve by elimination. Therefore, we'll use substitution. Let's solve for one term in one equation.

Now, we can substitute this expression into the second equation.

Now, we can substitute this value back into either of the original equations to find our solution. Let's use the simplest equation:

With these values, we see that our solution is the point .