Question

Algebra 1 > V.8 Solve a system of equations using substitution. Solve the system of equations using substitution:

4x + y = -15 and x - y = -15. What is the value of x in the solution to the system?

Answer 1

To solve the system of equations 4x + y = -15 and x - y = -15 using substitution, solve the second equation for y to get y = x + 15, substitute into the first equation, and then solve for x to find that x = -6. Subsequently, substituting x back into y = x + 15 gives y = 9, and the solution is (x, y) = (-6, 9).

Step-by-step explanation:

Solving the System of Equations by Substitution

To solve the given system of equations 4x + y = -15 and x - y = -15 using substitution, we first solve one of the equations for one variable and then substitute that into the other equation.

From the second equation, we can express y in terms of x: y = x + 15. This is now our substitution expression.

Substituting this expression into the first equation:

1. 4x + (x + 15) = -15
2. 5x + 15 = -15
3. 5x = -15 - 15
4. 5x = -30
5. x = −30/5
6. x = -6

The value of x in the solution to the system is -6.

Now, we can find the value of y by substituting x into the expression y = x + 15:

1. y = -6 + 15
2. y = 9

So the solution to the system of equations is (x, y) = (-6, 9).