Solve the system by substitution
2x + y = -11, 3x – 4y = 11
(3, 5)
(–5, –3)
(–3, –5)
(5, 3)
To solve the system of equations using substitution, we will solve one equation for one variable and substitute it into the other equation.
1. Let's solve the first equation, 2x + y = -11, for y:
y = -2x - 11
2. Now, substitute this expression for y in the second equation, 3x - 4y = 11:
3x - 4(-2x - 11) = 11
3. Simplify the equation:
3x + 8x + 44 = 11
11x + 44 = 11
4. Subtract 44 from both sides of the equation:
11x = -33
5. Divide both sides by 11 to solve for x:
x = -3
6. Now, substitute the value of x (-3) into the first equation to solve for y:
2(-3) + y = -11
-6 + y = -11
y = -11 + 6
y = -5
Therefore, the solution to the system of equations is (-3, -5).
To solve the system by substitution, we follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for y:
2x + y = -11
y = -2x - 11
Step 2: Substitute the expression obtained in Step 1 into the second equation, and solve for the remaining variable.
Replace y in the second equation with -2x - 11:
3x - 4(-2x - 11) = 11
Simplify the equation:
3x + 8x + 44 = 11
11x + 44 = 11
Subtract 44 from both sides:
11x = -33
Divide both sides by 11:
x = -3
Step 3: Substitute the value of x into either of the original equations, and solve for the other variable.
Let's substitute x = -3 into the first equation:
2(-3) + y = -11
-6 + y = -11
y = -11 + 6
y = -5
So the solution to the system of equations is (x, y) = (-3, -5).
Comparing this is the answer choices provided, the correct answer is (–3, –5).
from the first: y = -2x-11
into the 2nd
3x - 4(-2x-11) = 11
3x + 8x + 44 = 11
11x = -33
x = -3
No need to find y, the only one with x=-3 is the third one.
To make sure, sub (-3,-5) into both equations.