Use the graph below to estimate the solution to the system of equations shown.

Question

asked Jan 19, 2021 4.9k views

1 Answer

Cosaquee · Answer 1 · 2021-01-24T15:31:38+0000

Answer: The second choice is answer.

Explanation:

y=-x-3 (Slope is -1 and intercepts y at -3)

y=2x-8 (Slope is 2, to find y-intercept. Substitute x = 0 then we get -8) (For x-intercept, it's 4. Just substitute y=0 to get x-intercept.)

Because there are choices, it's easy to notice.

The first one, x = -4 and almost -5 which is not right. (x is around 1 almost 2.)

The second one, x = 1 and almost 2 is right.

The third one, x = -1 and almost -2 is not right (The intersection isn't even at -1 or any negative number for x-axis.)

The fourth one, just like the first one... x = 4 almost 5

$y=-x-3\\y=2x-8$

Substitute y=2x-8 in y=-x-3

$2x-8=-x-3\\2x-8+x+3=0\\3x-5=0\\3x=5\\x=(5)/(3)\\(x=1(2)/(3))$

Look at the value of x then find the answer that matches the value of x.

Now for y, substitute x = 5/3 in y = -x-3 (or in 2x-8 if you want.)

$y=-(5)/(3) -3\\y=-(5)/(3) -(9)/(3) \\y=-(14)/(3) \\(y=-4(2)/(3) )$

So the answer is the second choice.