Final answer:
The question involves solving a system of linear equations using the substitution method. The equations X = y - 7 and 3x - 4y = -24 are solved by substituting y - 7 for X in the second equation, resulting in X = -4 and y = 3 as the solution.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on the use of the substitution method to solve a system of linear equations.
The given system includes the equations X = y - 7 and 3x - 4y = -24. Here's a step-by-step guide to solve the system using substitution:
- Start with the provided equations:
X = y - 7
3x - 4y = -24 - Substitute the expression for X from the first equation into the second equation:
3(y - 7) - 4y = -24 - Simplify and solve for y:
3y - 21 - 4y = -24
-y = -24 + 21
-y = -3
y = 3 - Substitute the value of y back into the first equation to solve for X:
X = 3 - 7
X = -4
Therefore, the solution to the system of equations is X = -4 and y = 3.