Your friend asks for help on the following question:
Solve the system of equations using substitution:
{x + 7y = 02x − 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?
Next, substitute -7y for x in the second equation and solve for y. Then, substitute the value of y into the first equation to solve for x.
use x = -7y to get
2(-7y)-8y = 22
-14y-8y = 22
-22y = 22
y = -1
so x = -7y = 7
After rearranging the first equation for x and getting x = -7y, the next step is to substitute this value for x in the second equation. This will allow you to solve for y. Substituting x = -7y into the second equation, you get:
2(-7y) - 8y = 2
Now you can simplify and solve for y.
To solve the system of equations using substitution, your friend made progress by rearranging the first equation for x and obtaining x = -7y. The next step is to substitute this value of x into the second equation and solve for y. Here's how your friend can proceed:
1. Start with the second equation: 2x - 8y = 2.
2. Substitute x = -7y into the second equation: 2(-7y) - 8y = 2.
3. Simplify the equation: -14y - 8y = 2.
4. Combine like terms: -22y = 2.
5. Solve for y by dividing both sides of the equation by -22: y = 2 ÷ -22.
Note: Make sure your friend correctly divides both sides of the equation.
6. Simplify the value of y: y = -1/11.
Now that your friend has the value for y, they can substitute it back into the equation x = -7y to solve for x:
x = -7(-1/11).
x = 7/11.
Therefore, the solution to the system of equations is x = 7/11 and y = -1/11. Your friend successfully solved the system by using substitution.