Final answer:
To solve the system of equations, use the method of elimination by eliminating the y variable. Substitute the expression for x into one of the original equations to solve for y. The rounded solution to the system of equations is x = 147 and y = -59.
Step-by-step explanation:
To find the solution to the system of equations:
7.4x - y = -257
12.5x - y = -233
we can use the method of elimination. First, we will multiply the first equation by 12.5 and the second equation by 7.4 to eliminate the y variable:
93x - 12.5y = -3212.5
92.5x - 7.4y = -1724.2
Next, we subtract the second equation from the first to eliminate the y variable:
93x - 92.5x - 12.5y + 7.4y = -3212.5 - (-1724.2)
0.5x - 5.1y = -1488.3
Finally, we can solve for x by isolating the variable:
0.5x = -1488.3 + 5.1y
x = (-1488.3 + 5.1y) / 0.5
Now, we can substitute this expression for x into one of the original equations to solve for y. Let's use the first equation:
7.4((-1488.3 + 5.1y) / 0.5) - y = -257
Simplifying the equation gives:
55.6y - 1.1y = -3240
54.5y = -3240
y = -3240 / 54.5
y = -59.4
So, the solution to the system of equations is x = -1488.3 + 5.1(-59.4) / 0.5 and y = -59.4, which in rounded to the nearest whole number is x = 147 and y = -59.