Put the 10 steps in order that are used to solve the following systems of equations by substitution. and put what the answer whould be for each step
−7x−2y=−13 x−2y=11
1. Solve one of the equations for one variable in terms of the other variable.
-7x - 2y = -13
Solving for x:
x = (2y - 13) / -7
2. Substitute the expression for the variable in the other equation.
x - 2y = 11
Substituting (2y - 13) / -7 for x:
(2y - 13) / -7 - 2y = 11
3. Simplify the equation by expanding and combining like terms.
(2y - 13) / -7 - 2y = 11
(2y - 13 - 14y) / -7 = 11
(-12y - 13) / -7 = 11
4. Solve the equation for the remaining variable.
(-12y - 13) / -7 = 11
-12y - 13 = 11 * -7
-12y - 13 = -77
-12y = -77 + 13
-12y = -64
y = -64 / -12
y = 16/3 or approximately 5.33
5. Substitute the value of y into one of the original equations.
x - 2(16/3) = 11
x - 32/3 = 11
x = 11 + 32/3
x = 33/3 + 32/3
x = 65/3 or approximately 21.67
6. Write the solution as an ordered pair (x, y).
Solution: (65/3, 16/3) or approximately (21.67, 5.33)
Step 1: Solve one of the equations for one variable. Let's solve the second equation for x:
x - 2y = 11
Step 2: Isolate the variable.
x = 2y + 11
Step 3: Substitute into the other equation. Replace x in the first equation with the expression 2y + 11:
-7(2y + 11) - 2y = -13
Step 4: Distribute the -7 to the expression 2y + 11:
-14y - 77 - 2y = -13
Step 5: Combine like terms:
-16y - 77 = -13
Step 6: Move constant term to the opposite side of the equation:
-16y = 64
Step 7: Divide by the coefficient of y:
y = -4
Step 8: Substitute the value of y back into one of the original equations. Let's use the second equation:
x - 2(-4) = 11
Step 9: Simplify the equation:
x + 8 = 11
Step 10: Solve for x:
x = 3
So the solution to the system of equations is x = 3 and y = -4.
To solve the system of equations by substitution, follow these steps:
Step 1: Choose one of the equations to solve for one variable in terms of the other variable. Let's choose the second equation, x - 2y = 11, to solve for x.
Answer: x = 2y + 11
Step 2: Substitute the expression obtained from Step 1 into the other equation. Replace x in the first equation, −7x - 2y = −13, with 2y + 11.
Answer: -7(2y + 11) - 2y = -13
Step 3: Simplify the equation obtained in Step 2 by distributing and combining like terms.
Answer: -14y - 77 - 2y = -13
Step 4: Simplify further by combining like terms.
Answer: -16y - 77 = -13
Step 5: Move the constant term to the other side of the equation by adding 77 to both sides.
Answer: -16y = -13 + 77
Step 6: Simplify the equation obtained in Step 5.
Answer: -16y = 64
Step 7: Solve for y by dividing both sides of the equation by -16.
Answer: y = -4
Step 8: Substitute the value of y back into Step 1's expression to find x.
Answer: x = 2(-4) + 11
Step 9: Simplify the equation obtained in Step 8.
Answer: x = 3
Step 10: The solution to the system of equations is the ordered pair (x, y).
Answer: (3, -4)