Put the steps in order that are used to solve the following systems of equations by substitution. −7x−2y=−13
x−2y=11 don't give me steps in words just put the numbers in order
x - 2y = 11 --> x = 2y + 11
-16y = 64
-16y - 77 = -13
x - 2(-4) = 11
x + 8 = 11
y = -4
x = 3
-14y - 77 -2y = -13
-7 (2y + 11) -2y = -13
(3, -4)
-14y - 77 - 2y = -13
-7(2y + 11) - 2y = -13
-16y - 77 = -13
-16y = 64
y = -4
x - 2(-4) = 11
x + 8 = 11
x = 3
The steps in order to solve the system of equations by substitution are:
1. Rewrite one of the equations in terms of one variable.
2. Substitute the expression from step 1 into the other equation.
3. Solve the resulting equation for the variable.
4. Substitute the value of the variable from step 3 into one of the original equations to find the value of the other variable.
5. The solution is the values of the variables found in step 3 and step 4, represented as an ordered pair. In this case, the solution is (3, -4).
1. x - 2y = 11 (Rearranged to solve for x)
2. Substitute x = 2y + 11 into the first equation: -7x - 2y = -13
3. Simplify the equation: -7(2y + 11) - 2y = -13
4. Distribute: -14y - 77 - 2y = -13
5. Combine like terms: -16y - 77 = -13
6. Add 77 to both sides: -16y = 64
7. Divide by -16: y = -4
8. Substitute y = -4 into x - 2y = 11: x - 2(-4) = 11
9. Simplify the equation: x + 8 = 11
10. Subtract 8 from both sides: x = 3
11. The solution to the system is (x, y) = (3, -4)
To solve the given system of equations by substitution, follow these steps in order:
1. Rearrange one of the equations to isolate one variable in terms of the other variables. In this case, rearrange the second equation, x - 2y = 11, to solve for x: x = 2y + 11.
2. Substitute the expression for the isolated variable from step 1 into the other equation. Replace x in the first equation −7x - 2y = -13 with the expression 2y + 11: −7(2y + 11) - 2y = -13.
3. Simplify the resulting equation by distributing and combining like terms. −14y - 77 - 2y = -13 becomes -16y - 77 = -13.
4. Solve the equation from step 3 for the remaining variable. Solve -16y - 77 = -13 for y: -16y = -13 + 77 → -16y = 64 → y = -4.
5. Substitute the value of y obtained in step 4 into either of the original equations to solve for x. Using the first equation −7x - 2y = -13 and substituting y = -4: −7x - 2(-4) = -13, which simplifies to -7x + 8 = -13.
6. Solve the equation from step 5 for x: -7x = -13 - 8 → -7x = -21 → x = 3.
7. The solution to the system of equations is the ordered pair (x, y). Therefore, the solution for this given system of equations is (3, -4).