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 give me 10 steps
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)
1. Rewrite the second equation in terms of x to isolate x.
2. Multiply the coefficient of y in the first equation by -8 and set it equal to the constant term of the second equation.
3. Solve the equation from step 2 to find the value of y.
4. Substitute the value of y into the second equation to find the value of x.
5. Verify that the values of x and y satisfy the first equation.
6. Multiply the coefficient of y in the first equation by -2 and set it equal to the constant term of the second equation.
7. Solve the equation from step 6 to find the value of y.
8. Substitute the value of y into the second equation to find the value of x.
9. Verify that the values of x and y satisfy the second equation.
10. The solution to the system of equations is the point (x, y) where x = 3 and y = -4.
1) Rearrange one of the equations to solve for one variable in terms of the other variables. In this case, rearrange the second equation to solve for x: x = 2y + 11.
2) Substitute the expression for x from step 1 into the other equation. Replace x in the first equation with 2y + 11: -7(2y + 11) - 2y = -13.
3) Simplify the equation: -14y - 77 - 2y = -13.
4) Combine like terms: -16y - 77 = -13.
5) Move the constant term to the other side of the equation: -16y - 77 + 77 = -13 + 77.
6) Simplify the equation: -16y = 64.
7) Divide both sides of the equation by the coefficient of y: -16y / -16 = 64 / -16.
8) Solve for y: y = -4.
9) Substitute the value of y found in step 8 back into one of the original equations to solve for x. Replace y in x = 2y + 11 with -4: x = 2(-4) + 11.
10) Simplify the equation: x = -8 + 11.
11) Solve for x: x = 3.
Therefore, the solution to the system of equations is x = 3 and y = -4.
To solve the system of equations by substitution: -7x - 2y = -13 and x - 2y = 11, here are the steps in order:
1. Solve one of the equations for one variable in terms of the other. In this case, solve the second equation for x: x = 2y + 11.
2. Substitute the value of x from the previous step into the other equation. -7(2y + 11) - 2y = -13.
3. Simplify the equation by distributing and combining like terms: -14y - 77 - 2y = -13.
4. Combine like terms: -16y - 77 = -13.
5. Solve for y by isolating the variable: -16y - 77 + 77 = -13 + 77, which simplifies to -16y = 64.
6. Divide both sides of the equation by -16 to solve for y: -16y / -16 = 64 / -16, resulting in y = -4.
7. Substitute the value of y back into one of the original equations to solve for x: x - 2(-4) = 11.
8. Simplify the equation by distributing: x + 8 = 11.
9. Solve for x by isolating the variable: x + 8 - 8 = 11 - 8, which simplifies to x = 3.
10. The solution to the system of equations is (x, y) = (3, -4).
Note that the steps provided here are just one possible approach to solve the system of equations by substitution. There might be alternative methods or variations in the steps based on personal preference or different problem scenarios.