y = 2x + 4
2x - y = 6
Solve the system of equations using substitution.
A) (2,8)
B) (2,-8)
C) (10,24)
D) no solution <--
4x + 3y = 6
-4x + 2y = 14
olve the system of equations.
A) x = 1/2, y = 3
B) x = 3, y = 1/2 <-- or D?
C) x = 4, y = -3/2
D) x = -3/2, y = 4
#2 ... D?
Number 2 is D
N number one is correct
To solve the system of equations using substitution, you can follow these steps:
1. Solve one of the equations for one variable in terms of the other variable.
Let's take the first system of equations:
y = 2x + 4 (Equation 1)
2x - y = 6 (Equation 2)
From Equation 1, isolate y: y = 2x + 4.
2. Substitute the expression obtained in step 1 into the other equation.
Substitute y = 2x + 4 into Equation 2: 2x - (2x + 4) = 6.
3. Simplify and solve for the remaining variable.
Simplify the equation from step 2: 2x - 2x - 4 = 6.
-4 = 6.
The equation -4 = 6 is false, indicating that this system of equations has no solution.
Therefore, the correct answer is D) no solution.
Let's move on to the second system of equations:
1. Solve one of the equations for one variable in terms of the other variable.
Let's take the second system of equations:
4x + 3y = 6 (Equation 1)
-4x + 2y = 14 (Equation 2)
From Equation 1, isolate x: 4x = 6 - 3y, or x = (6 - 3y)/4.
2. Substitute the expression obtained in step 1 into the other equation.
Substitute x = (6 - 3y)/4 into Equation 2: -4(6 - 3y)/4 + 2y = 14.
3. Simplify and solve for the remaining variable.
Simplify the equation from step 2: -24 + 12y + 2y = 56.
Combine like terms: 14y - 24 = 56.
Add 24 to both sides: 14y = 80.
Divide by 14: y = 80/14, which simplifies to y = 40/7 or y = 5 5/7.
4. Substitute the value of y back into one of the original equations to solve for x.
Let's use Equation 1: 4x + 3(5 5/7) = 6.
Convert 5 5/7 to an improper fraction: 4x + (22+5)/7 = 6.
Simplify: 4x + 27/7 = 6.
Subtract 27/7 from both sides: 4x = 6 - 27/7.
Find a common denominator: 4x = 42/7 - 27/7.
Simplify: 4x = 15/7.
Divide by 4: x = 15/7 * 1/4.
Simplify: x = 15/28 or x = 0.5357 (rounded to four decimal places).
Therefore, the correct answer is B) x = 3 and y = 1/2.