Question

What is the solution to the system of equations graphed below?
y= -3/2x+12
y= 5x+ 28

Answer 1

Given:

The system of equations is
`y=-(3)/(2)x+12` and
`y=5x+28`

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;

`5x+28=-(3)/(2)x+12`

Simplifying, we get;

`(13)/(2)x+28=12`

`(13)/(2)x=-16`

`13x=-32`

`x=-2.462`

Thus, the value of x is -2.462

Substituting x = -2.462 in the equation
`y=5x+28`, we get;

`y=5(-2.462)+28`

`y=-12.31+28`

`y=15.69`

Thus, the value of y is 15.69.

Therefore, the solution to the system of the equations is (-2.462, 15.69)