### All SAT Math Resources

## Example Questions

### Example Question #1 : X And Y Intercept

Solve the equation for x and y.

x² + y = 31

x + y = 11

**Possible Answers:**

x = 13, 7

y = 8, –6

x = 6, 15

y = 5, –4

x = 8, –6

y = 13, 7

x = 5, –4

y = 6, 15

**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 #2 : X And Y Intercept

Solve the equation for x and y.

x² – y = 96

x + y = 14

**Possible Answers:**

x = 25, 4

y = 10, –11

x = 15, 8

y = 5, –14

x = 5, –14

y = 15, 8

x = 10, –11

y = 25, 4

**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 #3 : X And Y Intercept

Solve the equation for x and y.

5*x*² + *y* = 20

*x*² + 2*y* = 10

**Possible Answers:**

*x* = √10/3, –√10/3

*y* = 10/3

*x* = √4/5, 7

*y *= √3/10, 4

*x* = 14, 5

*y *= 4, 6

No solution

**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 Equation Of A Curve

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

*x*² + *y* = 60

*x –* *y* = 50

**Possible Answers:**

*x* = 40, 61

*y* = 11, –10

*x* = –40, –61

*y* = 10, –11

*x* = 11, –10

*y* = 40, 61

*x* = 10, –11

*y* = –40, –61

**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 #5 : X And Y Intercept

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

### Example Question #1 : How To Find X Or Y Intercept

If the equation of a line is 4*y* – *x* = 48, at what point does that line cross the *x*-axis?

**Possible Answers:**

(48,0)

(0,12)

(–48,0)

(0,–48)

(0,–12)

**Correct answer:**

(–48,0)

When the equation crosses the *x*-axis, *y* = 0. Plug 0 into the equation for *y*, and solve for *x*.

4(0) – *x* = 48, –*x* = 48, *x* = –48

### Example Question #2 : How To Find X Or Y Intercept

The slope of a line is equal to -3/4. If that line intersects the y-axis at (0,15), at what point does it intersect the x-axis?

**Possible Answers:**

60

15

20

-20

5

**Correct answer:**

20

If the slope of the line m=-3/4, when y=15 and x=0, plug everything into the equation y=mx+b.

Solving for b:

15=(-3/4)*0 + b

b=15

y=-3/4x + 15

To get the x-axis intersect, plug in y=0 and solve for x.

0 = -3/4x + 15

3/4x = 15

3x = 15*4

x = 60/3 = 20

x=20

### Example Question #3 : How To Find X Or Y Intercept

If these three points are on a single line, what is the formula for the line?

(3,3)

(4,7)

(5,11)

**Possible Answers:**

y = 3x - 9

y = 5x + 11

y = 4x + 31

y = 4x - 9

y = 3x - 3

**Correct answer:**

y = 4x - 9

Formula for a line: y = mx + b

First find slope from two of the points: (3,3) and (4,7)

m = slope = (y2 – y1) / x2 – x1) = (7-3) / (4-3) = 4 / 1 = 4

Solve for b by plugging m and one set of coordinates into the formula for a line:

y = mx + b

11 = 4 * 5 + b

11 = 20 + b

b = -9

y = 4x - 9

### Example Question #4 : How To Find X Or Y Intercept

The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?

**Possible Answers:**

(32,30)

(0,10)

(8,15)

(32,10)

(16, 10)

**Correct answer:**

(32,10)

y = mx + b

x intercept is 16 therefore one coordinate is (16,0)

0 = 5/8 * 16 + b

0 = 10 + b

b = -10

y = 5/8 x – 10

if x = 32

y = 5/8 * 32 – 10 = 20 – 10 = 10

Therefore (32,10)

### Example Question #5 : How To Find X Or Y Intercept

A line has the equation: x+y=1.

What is the y-intercept?

**Possible Answers:**

2

-1

0

0.5

1

**Correct answer:**

1

x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.