Question
Put the steps in order that are used to solve the following systems of equations by substitution.
−7x−2y=−13
x−2y=11
x-3
-16y-64
-14y-77-2y = -13
-7(2y+11)-2y= -13
x-2(-4)=11
-16y-77= -13
y= -4
(3,-4)
x-2y=11 x=2y +11
x+8=11
−7x−2y=−13
x−2y=11
x-3
-16y-64
-14y-77-2y = -13
-7(2y+11)-2y= -13
x-2(-4)=11
-16y-77= -13
y= -4
(3,-4)
x-2y=11 x=2y +11
x+8=11
Answers
GPT 3.5
1. Solve one of the equations for one variable in terms of the other (in this case, solve the second equation for x in terms of y: x = 2y + 11).
2. Substitute the expression found in step 1 for the variable in the other equation (substitute 2y + 11 for x in the first equation).
3. Solve the resulting equation for the remaining variable (in this case, solve -7(2y + 11) - 2y = -13 for y).
4. Substitute the value found in step 3 back into the expression from step 1 to solve for x (substitute the value of y in 2y + 11 for y in the expression x = 2y + 11).
5. Verify the solution by substituting the values of x and y back into both original equations to see if both equations are true.
2. Substitute the expression found in step 1 for the variable in the other equation (substitute 2y + 11 for x in the first equation).
3. Solve the resulting equation for the remaining variable (in this case, solve -7(2y + 11) - 2y = -13 for y).
4. Substitute the value found in step 3 back into the expression from step 1 to solve for x (substitute the value of y in 2y + 11 for y in the expression x = 2y + 11).
5. Verify the solution by substituting the values of x and y back into both original equations to see if both equations are true.
?
GPT 3.5
Apologies for the confusion. Here is the correct step-by-step process to solve the system of equations by substitution:
1. Solve one of the equations for one variable in terms of the other. Let's solve the second equation for x: x = 2y + 11.
2. Substitute the expression found in step 1 for the variable in the other equation. Replace x in the first equation with 2y + 11: -7(2y + 11) - 2y = -13.
3. Simplify and solve the resulting equation for the remaining variable. Distribute -7 through the parentheses and combine like terms: -14y - 77 - 2y = -13. Add 77 to both sides: -16y - 77 = -13. Add 77 to both sides: -16y = 64. Divide both sides by -16: y = -4.
4. Substitute the value found in step 3 back into the expression from step 1 to solve for x. Substitute -4 for y in x = 2y + 11: x = 2(-4) + 11. Simplify: x = -8 + 11. Solve: x = 3.
5. Verify the solution by substituting the values of x and y back into both original equations. The first equation becomes: -7(3) - 2(-4) = -13. Simplify: -21 + 8 = -13. This is true.
6. The second equation becomes: 3 - 2(-4) = 11. Simplify: 3 + 8 = 11. This is also true.
7. Thus, the solution to the system of equations is x = 3 and y = -4.
1. Solve one of the equations for one variable in terms of the other. Let's solve the second equation for x: x = 2y + 11.
2. Substitute the expression found in step 1 for the variable in the other equation. Replace x in the first equation with 2y + 11: -7(2y + 11) - 2y = -13.
3. Simplify and solve the resulting equation for the remaining variable. Distribute -7 through the parentheses and combine like terms: -14y - 77 - 2y = -13. Add 77 to both sides: -16y - 77 = -13. Add 77 to both sides: -16y = 64. Divide both sides by -16: y = -4.
4. Substitute the value found in step 3 back into the expression from step 1 to solve for x. Substitute -4 for y in x = 2y + 11: x = 2(-4) + 11. Simplify: x = -8 + 11. Solve: x = 3.
5. Verify the solution by substituting the values of x and y back into both original equations. The first equation becomes: -7(3) - 2(-4) = -13. Simplify: -21 + 8 = -13. This is true.
6. The second equation becomes: 3 - 2(-4) = 11. Simplify: 3 + 8 = 11. This is also true.
7. Thus, the solution to the system of equations is x = 3 and y = -4.
are you sure
GPT 3.5
Yes, I am sure of the steps I provided to solve the system of equations by substitution. If you have any specific concerns or questions about any step, please let me know and I'll be happy to clarify.