Question

-4y + 2z = -4
7y - z = -2

Answer 1

1) -4y+2z=-4

2) 7y-z=-2

First, change equation 2 so that 7y and -2 are equal to z

7y-z=-2

z-2=7y

z=7y+2

next, substitute z=7y+2 into equation 1)

-4y+2z=-4

-4y+2(7y+2)=-4

-4y+14y+4=-4

10y=-8

y=-8/10

y=-4/5

put y=-4/5 into equation 2)

z=7y+2

z=7(-4/5)+2

Convert 2 into fraction form

z=-28/5+10/5

z=-18/5

y=-4/5, z=-18/5

Answer 2

`\sf y =- (4)/(5) \textsf{Or } -0.8`

`\sf z = -(18)/(5) \textsf{ Or } -3.6`

Explanation:

To solve the system of equations:

• -4y + 2z = -4
• 7y - z = -2

We can use the method of any choice, such as substitution or elimination. I'll use the elimination method here.

First, let's multiply the second equation by 2 to make the coefficients of "z" in both equations cancel each other when summed:

-4y + 2z = -4

14y - 2z = -4

Now, add both equations:

(-4y + 2z) + (14y - 2z) = (-4) + (-4)

On the left side, the 2z and -2z terms cancel each other out:

-4y + 14y = -8

Combine like terms:

10y = -8

Now, divide both sides by 10 to solve for "y":

`\sf y =- (8)/(10)`

`\sf y =- (4)/(5) \textsf{Or } -0.8`

Now that we have the value of "y," we can substitute it into one of the original equations to solve for "z." Let's use equation second:

7y - z = -2

Substitute the value of "y":

`\sf 7* -(4)/(5) - z = -2`

Now, calculate:

`\sf -(28)/(5) - z = -2`

Isolate "z,"

`\sf -(28)/(5) +2 = z`

`\sf (-28 + 2 * 5)/(5) = z`

`\sf z = -(18)/(5) \textsf{ or } -3.6`

So, the solution to the system of equations is:

`\sf y =- (4)/(5) \textsf{Or } -0.8`

`\sf z = -(18)/(5) \textsf{ Or } -3.6`