To solve the given system of equations, set the two equations equal to each other and solve for the value of x. Then, substitute the value of x into either equation to find the corresponding value of y. The solution to the system is approximately x = 21/68 and y ≈ 11.1029.
To solve the system of equations:
y = 54x - 2
y = -14x + 19
1. Set the equations equal to each other: 54x - 2 = -14x + 19
2. Add 14x to both sides: 68x - 2 = 19
3. Add 2 to both sides: 68x = 21
4. Divide both sides by 68: x = 21/68
5. Substitute the value of x into either equation to find y: y = 54(21/68) - 2
6. Simplify: y = 891/68 - 2
7. Convert the fraction to a decimal: y ≈ 13.1029 - 2
8. Subtract: y ≈ 11.1029
Therefore, the solution to the system of equations is approximately x = 21/68 and y ≈ 11.1029.