Question

Solve the system by substitution. {2×+y=-11; 3×-4y=11

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system by substitution, we will solve one equation for one variable and substitute this expression into the other equation.

From the first equation, we have:

2x + y = -11

Solving for y, we get:

y = -11 - 2x

Now, we substitute this expression for y into the second equation:

3x - 4(-11 - 2x) = 11

Simplifying, we have:

3x + 44 + 8x = 11

Combining like terms:

11x + 44 = 11

Subtracting 44 from both sides:

11x = -33

Dividing by 11:

x = -3

Now, substitute this value of x back into the expression for y:

y = -11 - 2(-3)
y = -11 + 6
y = -5

Therefore, the solution to the system of equations is x = -3 and y = -5.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations by substitution, we will solve one equation for one variable and substitute that expression into the other equation.

Let's solve the first equation for x:

2x + y = -11.

To isolate x, subtract y from both sides:

2x = -11 - y.

Next, divide both sides by 2:

x = (-11 - y) / 2.

Now, substitute this expression for x into the second equation:

3x - 4y = 11.

Replace x with (-11 - y) / 2:

3((-11 - y) / 2) - 4y = 11.

Simplify the equation by distributing:

(-33 - 3y) / 2 - 4y = 11.

Multiply both sides by 2 to eliminate the fraction:

-33 - 3y - 8y = 22.

Combine like terms:

-33 - 11y = 22.

Add 33 to both sides:

-11y = 55.

Divide both sides by -11:

y = -5.

Now, substitute y = -5 into the first equation to find x:

2x + y = -11.

2x + (-5) = -11.

Simplify:

2x - 5 = -11.

Add 5 to both sides:

2x = -6.

Divide both sides by 2:

x = -3.

Therefore, the solution to the system of equations is x = -3 and y = -5.