Put the steps in order that are used to solve the following systems of equations by substitution.
{−7x −2y = −13x − 2y = 11
−7(2y+11)−2y=−13
(3,−4)
x−2y=11→ x=2y+11
−16y−77=−13
−14y−77−2y=−13
x=2(−4)+11→ x=3
1. Solve one equation for one variable (in this case, solve x=2y+11 from the second equation)
2. Substitute the solved equation into the other equation (in this case, substitute x=2y+11 into the first equation)
3. Solve the resulting equation for the remaining variable (in this case, solve for y)
4. Substitute the solved variable into either of the original equations (in this case, substitute y=-4 into either of the equations)
5. Solve for the remaining variable (in this case, solve for x)
6. Check the solution by plugging in the values for x and y into both original equations to ensure they are true.
The steps to solve the system of equations by substitution are as follows:
1. Rewrite one of the equations in terms of a single variable. In this case, we can rewrite the equation x - 2y = 11 as x = 2y + 11.
2. Substitute the expression found in step 1 into the other equation. Replace x in the equation -7x - 2y = -13 with 2y + 11.
3. Simplify the equation obtained after substitution.
-7(2y + 11) - 2y = -13
-14y - 77 - 2y = -13
-16y - 77 = -13
4. Solve the resulting equation for the variable y.
-16y - 77 = -13
-16y = -13 + 77
-16y = 64
y = 64 / -16
y = -4
5. Once you have found the value of y, substitute it back into one of the original equations to find the value of x. Using x - 2y = 11:
x = 2y + 11
x = 2(-4) + 11
x = -8 + 11
x = 3
6. The solution to the system of equations is (x, y) = (3, -4).
To solve a system of equations by substitution, follow these steps:
1. Rearrange one of the equations so that one variable is isolated. Let's start with the second equation: x - 2y = 11. Isolate x by adding 2y to both sides:
x = 2y + 11.
2. Substitute the expression for x in the other equation. Use the first equation: -7x - 2y = -13. Replace x with 2y + 11:
-7(2y + 11) - 2y = -13.
3. Simplify the equation by distributing the -7:
-14y - 77 - 2y = -13.
4. Combine like terms:
-16y - 77 = -13.
5. Isolate the variable. To do this, add 77 to both sides of the equation:
-16y - 77 + 77 = -13 + 77,
-16y = 64.
6. Solve for y by dividing both sides by -16:
y = 64 / -16,
y = -4.
7. Substitute the value of y back into one of the original equations to solve for x. Let's use the rearranged equation from step 1:
x = 2y + 11,
x = 2(-4) + 11,
x = -8 + 11,
x = 3.
Therefore, the solution to the system of equations is (3, -4).