Applications of linear systems
Interactive practice questions
The sum of two numbers is $56$56 and their difference is $30$30.
Set up two equations by letting $x$x and $y$y be the two numbers.
Use $x$x as the larger of the 2 numbers.
| Sum equation: | $\editable{}$ |
| Difference equation: | $\editable{}$ |
First solve for $x$x.
| Equation 1 | $x+y=56$x+y=56 |
| Equation 2 | $x-y=30$x−y=30 |
Now solve for $y$y.
The length of a rectangle measures $12$12 units more than the width, and the perimeter of the rectangle is $56$56 units.
Let $y$y be the width and $x$x be the length of the rectangle.
There are $36$36 members in a group, and the men outnumber the women by $16$16.
When comparing some test results Christa noticed that the sum of her Geography test score and Science test score was $172$172, and that their difference was $18$18.
Given that her Geography score is $x$x and her Science score is $y$y and she scored higher for the Geography test: