Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13 x−2y=11
1. Solve one of the equations for one variable in terms of the other variable. In this case, solve the second equation for x in terms of y: x = 2y + 11.
2. Substitute the expression found in step 1 into the other equation. Replace x in the first equation with (2y + 11): -7(2y + 11) - 2y = -13.
3. Solve the resulting equation for the remaining variable. Distribute the -7 to the terms inside the parentheses: -14y - 77 - 2y = -13. Combine like terms: -16y - 77 = -13.
4. Solve for y by isolating the variable. Add 77 to both sides: -16y = 64. Divide both sides by -16: y = -4.
5. Substitute the value of y into one of the original equations to solve for x. Use the second equation: x - 2(-4) = 11. Simplify: x + 8 = 11. Subtract 8 from both sides: x = 3.
6. Verify the solution by substituting the values of x and y into the other equation: -7(3) - 2(-4) = -13. Simplify: -21 + 8 = -13. The equation is true.
7. The solution to the system of equations is x = 3, y = -4.
To solve the given system of equations by substitution, follow these steps:
1. Start by rearranging one of the equations to solve for one variable in terms of the other.
For example: Solve the second equation for x: x = 2y + 11.
2. Substitute the expression for the variable found in step 1 into the other equation.
In this case, substitute x = 2y + 11 into the first equation: -7(2y + 11) - 2y = -13.
3. Simplify and solve the resulting equation from step 2 for the remaining variable.
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
4. Substitute the value found for y into one of the original equations to solve for the other variable.
Use the first equation: -7x - 2(-4) = -13
-7x + 8 = -13
-7x = -21
x = 3
5. Check the solution by substituting the values of x and y into both original equations.
−7(3)−2(-4) = -13 [satisfied]
3−2(-4) = 11 [satisfied]
Therefore, the solution to the system of equations is x = 3 and y = -4.
To solve a system of equations by substitution, follow these steps:
Step 1: Choose one equation to solve for one variable in terms of the other variable.
In this case, let's solve the second equation, x - 2y = 11, for x in terms of y:
x = 2y + 11.
Step 2: Substitute the expression for the variable found in Step 1 into the other equation.
Substitute x = 2y + 11 into the first equation, -7x - 2y = -13:
-7(2y + 11) - 2y = -13.
Step 3: Simplify and solve the resulting equation for the remaining variable.
Distribute -7 on 2y + 11 and combine like terms:
-14y - 77 - 2y = -13.
-16y - 77 = -13.
-16y = -13 + 77.
-16y = 64.
Divide both sides by -16:
y = -4.
Step 4: Substitute the value of y found in Step 3 back into one of the original equations to solve for the other variable.
Substitute y = -4 into x - 2y = 11:
x - 2(-4) = 11.
x + 8 = 11.
Subtract 8 from both sides:
x = 3.
So, the solution to the system of equations -7x - 2y = -13 and x - 2y = 11 is x = 3 and y = -4.