1. Rearrange one of the equations to solve for one variable in terms of the other.
2. Substitute the value obtained in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value obtained in step 3 into one of the original equations to solve for the other variable.
5. Repeat steps 1-4 for any additional variables.
6. Check the solution by substituting the values obtained in the original equations and verifying that they satisfy each equation.
Put the steps in order that are used to solve the following systems of equations by substitution.
−7x−2y=−13 and x−2y=11
x-2y=11--> x=2y+11
-7(2y+11)-2y=13
-16y=64,(3,-4)
x=3, x-2(-4)=11
-16-77=-13
y=-4
x+8=11
-14y-77-2y=-13
7 answers
put the numbers in order
1. x-2y=11
2. x=2y+11
3. -7(2y+11)-2y=13
4. -16y=64
5. y=-4
6. x+8=11
7. -14(-4)-77-2(-4)=-13
8. (3, -4)
2. x=2y+11
3. -7(2y+11)-2y=13
4. -16y=64
5. y=-4
6. x+8=11
7. -14(-4)-77-2(-4)=-13
8. (3, -4)
10 steps
1. Rearrange the first equation to solve for x in terms of y: x = 2y + 11
2. Substitute the value of x from step 1 into the second equation: (2y + 11) - 2y = 11.
3. Simplify the equation from step 2: 11 = 11.
4. Since the equation in step 3 is always true, the system of equations has infinitely many solutions.
5. There is no need to solve for the values of x and y further.
6. The system of equations is consistent.
7. The equations describe a dependent system.
8. The graph of the equations is a line.
9. The graph of the equations intersects at every point along the line.
10. The system of equations is not overdetermined or underdetermined.
2. Substitute the value of x from step 1 into the second equation: (2y + 11) - 2y = 11.
3. Simplify the equation from step 2: 11 = 11.
4. Since the equation in step 3 is always true, the system of equations has infinitely many solutions.
5. There is no need to solve for the values of x and y further.
6. The system of equations is consistent.
7. The equations describe a dependent system.
8. The graph of the equations is a line.
9. The graph of the equations intersects at every point along the line.
10. The system of equations is not overdetermined or underdetermined.
wrong
I apologize for the confusion. Here are the correct steps in order to solve the given system of equations by substitution:
1. Start with the given equations:
-7x - 2y = -13 (Equation 1)
x - 2y = 11 (Equation 2)
2. Solve Equation 2 for x in terms of y:
x = 2y + 11
3. Substitute the expression for x (from step 2) into Equation 1:
-7(2y + 11) - 2y = -13
4. Simplify the equation from step 3:
-14y - 77 - 2y = -13
5. Combine like terms:
-16y - 77 = -13
6. Add 77 to both sides of the equation:
-16y = 64
7. Divide both sides of the equation by -16:
y = -4
8. Substitute the value of y (from step 7) into Equation 2 to find x:
x - 2(-4) = 11
9. Simplify the equation from step 8:
x + 8 = 11
10. Subtract 8 from both sides of the equation:
x = 3
Therefore, the solution to the system of equations is:
x = 3
y = -4
1. Start with the given equations:
-7x - 2y = -13 (Equation 1)
x - 2y = 11 (Equation 2)
2. Solve Equation 2 for x in terms of y:
x = 2y + 11
3. Substitute the expression for x (from step 2) into Equation 1:
-7(2y + 11) - 2y = -13
4. Simplify the equation from step 3:
-14y - 77 - 2y = -13
5. Combine like terms:
-16y - 77 = -13
6. Add 77 to both sides of the equation:
-16y = 64
7. Divide both sides of the equation by -16:
y = -4
8. Substitute the value of y (from step 7) into Equation 2 to find x:
x - 2(-4) = 11
9. Simplify the equation from step 8:
x + 8 = 11
10. Subtract 8 from both sides of the equation:
x = 3
Therefore, the solution to the system of equations is:
x = 3
y = -4