Final answer:
To solve the linear system of equations, you can use either the substitution or elimination method. The solution to the system is x = 2, y = 3.
Step-by-step explanation:
To solve the linear system of equations:
y = 5x - 7
-4x + y = -1
15x + y = 70
3x - 2y = -8
We will use the substitution or elimination method.
1. Substitution Method:
-4x + (5x - 7) = -1. Simplify and solve for x: x = 2.
Substitute x = 2 into the other equation: y = 5(2) - 7 = 3.
The solution to the system is x = 2, y = 3.
2. Elimination Method:
Multiply the second equation by 5 and the fourth equation by 4 to get:
-20x + 5y = -5
12x - 8y = -32
Adding these two equations together eliminates y, solve for x: x = 2.
Substitute x = 2 into the third equation: 15(2) + y = 70. Solve for y: y = 3.
The solution to the system is x = 2, y = 3.