Given:
The system of equations is [tex]y=-\frac{3}{2}x+12[/tex] and [tex]y=5x+28[/tex]
We need to determine the solution to the system of equations.
Solution:
The solution to the system of equations is the point of intersection of these two lines.
Let us solve the system of equations using substitution method.
Thus, we have;
[tex]5x+28=-\frac{3}{2}x+12[/tex]
Simplifying, we get;
[tex]\frac{13}{2}x+28=12[/tex]
[tex]\frac{13}{2}x=-16[/tex]
[tex]13x=-32[/tex]
[tex]x=-2.462[/tex]
Thus, the value of x is -2.462
Substituting x = -2.462 in the equation [tex]y=5x+28[/tex], we get;
[tex]y=5(-2.462)+28[/tex]
[tex]y=-12.31+28[/tex]
[tex]y=15.69[/tex]
Thus, the value of y is 15.69.
Therefore, the solution to the system of the equations is (-2.462, 15.69)
