Review the following information about vectors q and r. What is the value of a?
q=(-4,1)
31
r = (a, 3)
7(q + r) = (-35, 28)
-5

Work Shown:

q = (-4, 1) is one vector

r = (a,3) is another vector

The resultant vector is

q+r = (-4,1)+(a,3)

q+r = (-4+a,1+3)

q+r = (-4+a,4)

Multiply both sides by 7

7(q+r) = 7*(-4+a,4)

7(q+r) = (7*(-4+a),7*4)

7(q+r) = (-28+7a, 28)

Since 7(q+r) = (-35, 28), we know that,

(-28+7a, 28) =  (-35, 28)

which leads to

-28 + 7a = -35

when we equate the x components of each vector. Let's solve for 'a'

-28 + 7a = -35

7a = -35+28

7a = -7

a = -7/7

a = -1

Check:

q = (-4,1)

r = (a,3) = (-1,3)

q+r = (-4,1)+(-1,3)

q+r = (-4+(-1), 1+3)

q+r = (-5, 4)

7*(q+r) = 7*(-5, 4)

7*(q+r) = (7*(-5), 7*4)

7*(q+r) = (-35, 28)

The answer is confirmed.

x + 4/7

step-by-step explanation:

use cymath

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.