Solve the system of equations using elimination: 4, x, plus, 4, y, equals, 124x+4y=12 and 4, x, plus, 7, y, equals, 244x+7y=24
To solve the system of equations using elimination, we need to eliminate one of the variables by multiplying one or both of the equations by a factor so that the coefficients of either x or y will be the same.
Let's start by multiplying the first equation by 7 and the second equation by 4 to make the coefficients of x the same:
7(124x + 4y) = 7(12)
4(244x + 7y) = 4(24)
This simplifies to:
868x + 28y = 84
976x + 28y = 96
Now, subtract the first equation from the second equation:
(976x + 28y) - (868x + 28y) = 96 - 84
108x = 12
Divide both sides of the equation by 108:
x = 12/108
x = 1/9
Now, substitute this value of x back into either of the original equations. Let's use the first equation:
124(1/9) + 4y = 12
(124/9) + 4y = 12
Multiply both sides of the equation by 9 to get rid of the fraction:
124 + 36y = 108
36y = 108 - 124
36y = -16
y = -16/36
y = -4/9
Therefore, the solution to the system of equations is x = 1/9 and y = -4/9.