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 $y=-\frac{3}{2}x+12$ 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;

$5x+28=-\frac{3}{2}x+12$

Simplifying, we get;

$\frac{13}{2}x+28=12$

       $\frac{13}{2}x=-16$

       $13x=-32$

          $x=-2.462$

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)