Explanation:
Let x be mixture x liters and y be mixture y liters.
We need a total of 4 liters so
![x + y = 4](https://img.qammunity.org/2023/formulas/mathematics/college/40r7h8psfnqapwredzmvphl994qzkycglt.png)
Mixture x is 20% saline solution
Mixture Y is a 10% saline solution
4 liters of a 15% saline solution is 60% saline solution.
![.20x + .10y = 0.6](https://img.qammunity.org/2023/formulas/mathematics/high-school/lpwkwo7gtidpup8jdbl05klg2vdzqy80vc.png)
So a is the system of equations,
Using Elimination, eliminate the variable x.
![- 5(.20x + .10y) = 0.6](https://img.qammunity.org/2023/formulas/mathematics/high-school/31wwbw5lbjyllzq2ofqrvtyzyw3jqccluf.png)
![( - x - .50y) = - 3](https://img.qammunity.org/2023/formulas/mathematics/high-school/p2x83dedkanvkdk68xiucn0zncgwdkh1jc.png)
Add to the first system.
![0.50y = 1](https://img.qammunity.org/2023/formulas/mathematics/high-school/aekkzenlblng1glcl70cswyvupozm3mjp9.png)
![y = 2](https://img.qammunity.org/2023/formulas/mathematics/college/llodm37v2wx1i7jasgsny6f9p8usrh5ghp.png)
Plug this into the of system of equations, to find x
![x + 2 = 4](https://img.qammunity.org/2023/formulas/mathematics/high-school/lchvvb8siy9rx2zmrpaqwebeqs29jpdjwa.png)
![x = 2](https://img.qammunity.org/2023/formulas/mathematics/high-school/h1w3uombpcqus9of954w06kunwejo2ltg4.png)
So our solution is (2,2) We would need 2 liters of Mixture X and 2 liters of Mixture Y