Question

Which is the approximate solution to the system y = 0.5x + 3.5 and y = − 2/3 x + 1/3 shown on the graph? (–2.7, 2.1) (–2.1, 2.7) (2.1, 2.7) (2.7, 2.1)

Answer 1

(–2.7, 2.1)

Explanation:

edg. 2020 unit test

Answer 2

The approximate solution to the system is
`(-2.7, 2.1)`.

Explanation:

To solve the system of equations
`\begin{bmatrix}y=0.5x+3.5\\ y=-(2)/(3)x+(1)/(3)\end{bmatrix}` you must:

`\mathrm{Rationalize\:equations}\\\\\begin{bmatrix}y=\left((1)/(2)\right)x+\left((7)/(2)\right)\\ y=-(2)/(3)x+(1)/(3)\end{bmatrix}`

`\mathrm{Subsititute\:}y=-(2)/(3)x+(1)/(3)\\\\\begin{bmatrix}-(2)/(3)x+(1)/(3)=(1)/(2)x+(7)/(2)\end{bmatrix}`

`\mathrm{Isolate}\:x\:\mathrm{for}\:-(2)/(3)x+(1)/(3)=(1)/(2)x+(7)/(2)\\\\-(2)/(3)x=(19)/(6)+(1)/(2)x\\\\-(7)/(6)x=(19)/(6)\\\\6\left(-(7)/(6)x\right)=(19\cdot \:6)/(6)\\\\-7x=19\\\\x=-(19)/(7)\approx-2.7`

`\mathrm{For\:}y=-(2)/(3)x+(1)/(3)\\\\\mathrm{Subsititute\:}x=-(19)/(7)\\\\y=-(2)/(3)\left(-(19)/(7)\right)+(1)/(3)\\\\y=(15)/(7)\approx 2.1`

The approximate solutions to the system of equations are:

`x=-2.7 ,\:y=2.1`