Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13 x−2y=11 (10 points)
y = -4
x = 3
(3,-4)
x -2y = 11 --> x = 2y + 11
x - 2(-4) = 11
x + 8 = 11
-14y - 77 - 2y = -13
-16y = 64
-16y - 77 =-13
-7(2y + 11) - 2y = -13
1. Rewrite one of the equations in terms of one variable (in this case, x = 2y + 11).
2. Substitute the expression for that variable into the other equation.
3. Solve the resulting equation for the remaining variable (in this case, y).
4. Substitute the value of y back into the equation x = 2y + 11 to find the value of x.
5. Check the solution by substituting the values of x and y into both original equations to see if they are true.
6. Write the final solution as an ordered pair (x, y).
To solve the system of equations using substitution, follow these steps in order:
1. Start with the given system of equations:
-7x - 2y = -13
x - 2y = 11
2. Solve one equation for one variable. Looking at the second equation, solve for x:
x = 2y + 11
3. Substitute the expression for x into the other equation:
-7(2y + 11) - 2y = -13
4. Simplify the equation by distributing and combining like terms:
-14y - 77 - 2y = -13
-16y - 77 = -13
5. Solve the equation for the variable y:
-16y = -13 + 77
-16y = 64
y = 64 / -16
y = -4
6. Substitute the value of y back into one of the original equations to solve for x. Let's use the second equation:
x - 2(-4) = 11
x + 8 = 11
x = 11 - 8
x = 3
7. Therefore, the solution to the system of equations is x = 3 and y = -4, or in ordered pair form (3, -4).
To solve the system of equations by substitution, follow these steps:
Step 1: Choose one equation and solve it for one variable in terms of the other variable.
- In this case, the equation x - 2y = 11 can be solved for x as x = 2y + 11.
Step 2: Substitute the expression obtained in step 1 for the variable in the other equation.
- Substitute x = 2y + 11 into the equation -7x - 2y = -13.
Step 3: Simplify and solve the resulting equation.
- Simplifying -7x - 2y = -13 by substituting x = 2y + 11 gives:
-7(2y + 11) - 2y = -13.
Solve this equation for y.
Step 4: Substitute the value of y obtained in step 3 into one of the original equations to find the corresponding value of x.
- Put the value of y back into either of the original equations and solve for x.
By following these steps, you will be able to find the solutions for the given system of equations. In this case, the solutions are x = 3 and y = -4, or (3, -4) in coordinate form.