Solve the system using elimination.
5x = –25 + 5y
10y = 42 + 2x
(–1, 4)
(4, –1)
(–1, 2)
(5, 10)
To solve the system using elimination, we need to eliminate one variable by manipulating the equations. Let's start by multiplying the first equation by 2 and the second equation by 5 to make the coefficients of y equal:
2(5x) = 2(-25 + 5y)
5(10y) = 5(42 + 2x)
Simplifying both equations:
10x = -50 + 10y
50y = 210 + 10x
To eliminate x, we can subtract the first equation from the second:
50y - 10x = 210 + 10x - (-50 + 10y)
50y - 10x = 210 + 10x + 50 - 10y
50y - 10x = 260 - y
Rearranging the terms:
50y + y - 10x = 260
51y - 10x = 260
Now, we have a new equation:
51y - 10x = 260
To solve for x, we can multiply the first equation by 10 and add it to the second equation:
10(10x) = 10(-50 + 10y)
51y - 10x = 260
This gives us:
100x = -500 + 100y
51y - 10x = 260
Adding these equations:
100x + (-10x) = -500 + 100y + 260
90x = 100y - 240
9x = 10y - 24
Now we have a new equation:
9x = 10y - 24
Substituting this equation back into the first equation:
9x = 10y - 24
9x = 9(4) - 24
9x = 36 - 24
9x = 12
x = 12/9
x = 4/3
Substituting the value of x into the second equation:
10y = 42 + 2x
10y = 42 + 2(4/3)
10y = 42 + 8/3
10y = (126 + 8)/3
10y = 134/3
y = (134/3)/10
y = 134/30
y = 67/15
Therefore, the solution to the system of equations is (x, y) = (4/3, 67/15). However, none of the given answer choices match this solution.