Question

Your friend asks for help on the following question:

Solve the system of equations using substitution:

{x + 7y = 0
{2x − 8y = 22

Your friend says they want to rearrange the first equation for x and get x = -7y, but now they are stuck. What needs to be done next? ______________.

After doing this, you will now have _____.


You tell your friend to remember that substitution means to replace. So we are replacing ____ with ____.

Final answer is __________.

Answer 1

Answer: (7,-1)

Explanation:

`\displaystyle\\\left \{ {{x+7y=0} \atop {2x-8y=22}} \right. \\\\\\\left \{ {{x+7y-7y=0+(-7y)} \atop {2x-8y=22}} \right. \\\\\\\left \{ {{x=-7y\ \ \ \ (1)} \atop {2x-8y=22\ \ \ \ (2)}} \right.`

Let us substitute the value of x=-7y into equation (2):

2(-7y)-8y=22

-14y-8y=22

-22y=22

Divide both parts of the equation by -22:

y=-1

Let us substitute the value of y=-1 into equation (1):

x=-7(-1)

x=7