Question

The table gives some values of x and their corresponding values of y for the graphs of lines l and k in the x-y plane. the system of equations consisting of the equations for the lines l and k has solution (x,y). what is the ordered pair that is the solution of this system?​

A. (-1,2)
B. (0.5,6.5)
C. (1.5,5.5)
D. (3,10)

Answer 1

C. (1.5, 5.5)

Step-by-step explanation:

✔️Equation of line l in slope-intercept form, y = mx + b

y-intercept (b) = 7 (the value of y when x = 0)

Slope (m) = ∆y/∆x

Using (0, 7) and (1, 6)

Slope (m) = (6 - 7)/(1 - 0) = -1/1 = -1

Substitute m = -1 and b = 7 into y = mx + b

Equation: y = -x + 7

✔️Equation of line k in slope-intercept form, y = mx + b

y-intercept (b) = 1 (the value of y when x = 0)

Slope (m) = ∆y/∆x

Using (0, 1) and (1, 4)

Slope (m) = (4 - 1)/(1 - 0) = 3/1 = 3

Substitute m = 3 and b = 1 into y = mx + b

Equation: y = 3x + 1

✔️Solve the system of equations:

y = -x + 7 => Eqn. 1

y = 3x + 1 => Eqn. 2

Substute y = (-x + 7) in Eqn. 2

-x + 7 = 3x + 1

Collect like terms

-x - 3x = -7 + 1

-4x = -6

-4x/-4 = -6/-4

x = 1.5

Substitute x = 1.5 in eqn. 1

y = -1.5 + 7

y = 5.5

✅Solution = (1.5, 5.5)