Put these steps into order that are used to solve the following systems of equations by substitution.
-7x -2y = - 13
x - 2y = 11
(Only use the numbers below and put them in order.)
• -7(2y+11)-2y=-13
• x+8=11
• x - 2y = 11 —> x = 2y + 11
• -16y - 77 = -13
• x = 3
• -14y - 17 -2y = -13
• y = -4
• -16y = 64
• x - 2 (-4) = 11
• (3,-4)
1. Rearrange one equation to solve for one variable in terms of the other variable, for example: x = 2y + 11.
2. Substitute the expression from step 1 into the other equation, replacing the variable that was solved for. This yields a new equation with only one variable.
3. Solve the new equation for the remaining variable.
4. Substitute the value of the remaining variable back into the expression from step 1 to find the value of the other variable.
5. Write the solution as an ordered pair (x,y) where x and y are the values found in step 3 and step 4 respectively.
1. x - 2y = 11 —> x = 2y + 11
2. Substitute the expression for x in the first equation: -7(2y+11)-2y=-13
3. Simplify: -14y - 154 - 2y = -13
4. Combine like terms: -16y - 154 = -13
5. Move the constant term to the other side: -16y = 141
6. Divide by -16: y = -4
7. Substitute the value of y into the second equation to solve for x: x - 2 (-4) = 11
8. Simplify: x + 8 = 11
9. Move the constant term to the other side: x = 3
10. The solution is (x, y) = (3, -4)
To solve the system of equations by substitution, follow these steps in order:
1. Start with the given equations:
-7x - 2y = -13
x - 2y = 11
2. 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
3. Substitute the expression from step 2 into the other equation. Replace x in the first equation with (2y + 11):
-7(2y + 11) - 2y = -13
4. Simplify the equation by distributing and combining like terms:
-14y - 77 - 2y = -13
-16y - 77 = -13
5. Continue solving for y:
-16y = -13 + 77
-16y = 64
6. Divide by -16 to isolate y:
y = 64 / -16
y = -4
7. Substitute the value of y into the equation obtained in step 2 to solve for x:
x = 2(-4) + 11
x = -8 + 11
x = 3
8. The solution to the system of equations is (x, y) = (3, -4).
Therefore, the correct order of steps is:
-7(2y+11)-2y=-13
x=2y+11
-16y-77=-13
y=-4
-16y=64
x=3
(3, -4)