Question

Consider the system of equations given in slope-intercept form. y = −13x + 17, y = 5x - 23 The solution seems to be about (8, 14). Use the graphing calculator to find the exact values for the intersection point. What is the solution to this system of equations?

Answer 1

To find the solution to the given system of equations, we can solve them using various methods, such as substitution or elimination. In this case, we can set the two equations equal to each other and solve for x. The resulting x-value can then be substituted into either equation to find the corresponding y-value. The solution to the system is (20/9, -107/9).

Step-by-step explanation:

To find the exact values for the intersection point of the two lines, we need to solve the system of equations. The given equations are:

y = -13x + 17

y = 5x - 23

To solve the system, we can set the equations equal to each other:

-13x + 17 = 5x - 23

Combine like terms:

-13x - 5x = -23 - 17

-18x = -40

Divide both sides by -18:

x = 40/18 = 20/9

Substitute the x-value into either equation to find y:

y = -13(20/9) + 17 = -260/9 + 153/9 = -107/9

Therefore, the solution to the system of equations is (20/9, -107/9).

Answer 2

The exact solution for this equation would be (2.222, -11.889)

Step-by-step explanation:

Since it told us to use a graphing calculator, I went on to desmos graphing calculator, typed in the equation, then I found out where the two line intersect, and then that was the answer.