Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16(1 point)
We can solve the system of equations using substitution as follows:
1. Solve the first equation for y in terms of x:
y = 2 + 3x
2. Substitute this expression for y in the second equation, then solve for x:
4x - 3y = -16
4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2
3. Substitute the value of x into either equation to solve for y:
y = 2 + 3x
y = 2 + 3(2)
y = 8
Therefore, the system of equations is solved and the solution is (x, y) = (2, 8).
Solve the system of equations. 2x%2B6y%3D−18 x%3D5y−1(1 point) Responses (−7.25%2C −1.25) left parenthesis negative 7.25 comma negative 1.25 right parenthesis (5.25%2C 1.25) left parenthesis 5.25 comma 1.25 right parenthesis (−6%2C −1) left parenthesis negative 6 comma negative 1 right parenthesis (4%2C 1)
To solve the system of equations using substitution, we'll start by solving one equation for a variable and then substituting that expression into the other equation.
Given the equations:
1) y = 2 + 3x
2) 4x - 3y = -16
Step 1: Solve equation 1 for y
In equation 1, y is already isolated, so we can directly use it.
Step 2: Substitute the expression for y into equation 2
Replace y in equation 2 with the expression from equation 1:
4x - 3(2 + 3x) = -16
Step 3: Simplify and solve for x
Distribute the negative sign to simplify the equation:
4x - 6 - 9x = -16
Combine like terms:
-5x - 6 = -16
Add 6 to both sides to isolate the x-term:
-5x = -10
Divide by -5 to solve for x:
x = 2
Step 4: Substitute the value of x back into equation 1 to solve for y
Using the value of x in equation 1:
y = 2 + 3(2)
y = 2 + 6
y = 8
So the solution to the system of equations is x = 2 and y = 8.