What is the value of x in the solution to the system y = 4x + 3 and 3x + 2y = -16? (Round to the nearest integer if necessary.)
Get equations in same form first.
3x + 2y = -16
4x - y = -3
Multiply second equation by 2.
8x - 2y = -6
Add the two equations.
11x = -22
x = -2
To find the value of x in the solution to the system of equations, we need to solve the system of equations simultaneously. We can use the method of substitution or elimination to solve the system.
Let's solve the system using the method of substitution:
Step 1: Start with the first equation: y = 4x + 3
Step 2: Substitute this expression for y in the second equation: 3x + 2(4x + 3) = -16
Step 3: Simplify the equation: 3x + 8x + 6 = -16
Step 4: Combine like terms: 11x + 6 = -16
Step 5: Move the constant term to the other side of the equation by subtracting 6 from both sides: 11x = -22
Step 6: Divide both sides by 11 to solve for x: x = -22/11
Step 7: Simplify the result: x = -2
Therefore, the value of x in the solution to the system of equations is x = -2 (rounded to the nearest integer).