### All SAT Math Resources

## Example Questions

### Example Question #51 : Geometry

Solve the equation for x and y.

x² + y = 31

x + y = 11

**Possible Answers:**

x = 8, –6

y = 13, 7

x = 6, 15

y = 5, –4

x = 5, –4

y = 6, 15

x = 13, 7

y = 8, –6

**Correct answer:**

x = 5, –4

y = 6, 15

Solving the equation follows the same system as the first problem. However since x is squared in this problem we will have two possible solutions for each unknown. Again substitute y=11-x and solve from there. Hence, x2+11-x=31. So x2-x=20. 5 squared is 25, minus 5 is 20. Now we know 5 is one of our solutions. Then we must solve for the second solution which is -4. -4 squared is 16 and 16 –(-4) is 20. The last step is to solve for y for the two possible solutions of x. We get 15 and 6. The graph below illustrates to solutions.

### Example Question #1 : How To Find The Equation Of A Curve

Solve the equation for x and y.

x² – y = 96

x + y = 14

**Possible Answers:**

x = 15, 8

y = 5, –14

x = 5, –14

y = 15, 8

x = 10, –11

y = 25, 4

x = 25, 4

y = 10, –11

**Correct answer:**

x = 10, –11

y = 25, 4

This problem is very similar to number 2. Derive y=14-x and solve from there. The graph below illustrates the solution.

### Example Question #2 : How To Find The Equation Of A Curve

Solve the equation for x and y.

5*x*² + *y* = 20

*x*² + 2*y* = 10

**Possible Answers:**

*x* = 14, 5

*y *= 4, 6

No solution

*x* = √4/5, 7

*y *= √3/10, 4

*x* = √10/3, –√10/3

*y* = 10/3

**Correct answer:**

*x* = √10/3, –√10/3

*y* = 10/3

The problem involves the same method used for the rest of the practice set. However since the x is squared we will have multiple solutions. Solve this one in the same way as number 2. However be careful to notice that the y value is the same for both x values. The graph below illustrates the solution.

### Example Question #1 : How To Find The Slope Of Perpendicular Lines

Solve the equation for *x* and *y*.

*x*² + *y* = 60

*x –* *y* = 50

**Possible Answers:**

*x* = 10, –11

*y* = –40, –61

*x* = 40, 61

*y* = 11, –10

*x* = 11, –10

*y* = 40, 61

*x* = –40, –61

*y* = 10, –11

**Correct answer:**

*x* = 10, –11

*y* = –40, –61

This is a system of equations problem with an x squared, to be solved just like the rest of the problem set. Two solutions are required due to the x2. The graph below illustrates those solutions.

### Example Question #61 : Geometry

A line passes through the points and . What is the equation for the line?

**Possible Answers:**

None of the available answers

**Correct answer:**

First we will calculate the slope as follows:

And our equation for a line is

Now we need to calculate b. We can pick either of the points given and solve for

Our equation for the line becomes