Answer:
The solution to the system of equations is:
[tex]x=\frac{25}{3},\:y=-\frac{11}{9}[/tex]
Step-by-step explanation:
Given the system of equations
[tex]5x + 3y = 38[/tex]
[tex]2x + 3y = 13[/tex]
solving the system of equations
[tex]\begin{bmatrix}5x+3y=38\\ 2x+3y=13\end{bmatrix}[/tex]
Multiply 5x+3y=38 by 2: 10x+6y=76
Multiply 2x+3y=13 by 5: 10x+15y=65
[tex]\begin{bmatrix}10x+6y=76\\ 10x+15y=65\end{bmatrix}[/tex]
so
[tex]10x+15y=65[/tex]
[tex]-[/tex]
[tex]\underline{10x+6y=76}[/tex]
[tex]9y=-11[/tex]
now solving 9y = -11 for y
[tex]9y=-11[/tex]
divide both sides by 9
[tex]\frac{9y}{9}=\frac{-11}{9}[/tex]
Simplify
[tex]y=-\frac{11}{9}[/tex]
For 10x+6y=76 plug in y = -11/9
[tex]10x+6\left(-\frac{11}{9}\right)=76[/tex]
subtract 6(-11/9) from both sides
[tex]10x+6\left(-\frac{11}{9}\right)-6\left(-\frac{11}{9}\right)=76-6\left(-\frac{11}{9}\right)[/tex]
[tex]10x=\frac{250}{3}[/tex]
Divide both sides by 10
[tex]\frac{10x}{10}=\frac{\frac{250}{3}}{10}[/tex]
[tex]x=\frac{25}{3}[/tex]
Therefore, the solution to the system of equations is:
[tex]x=\frac{25}{3},\:y=-\frac{11}{9}[/tex]
