-5x+7y=67
11x+12y=17
what is the solution for the system of equations above
To find the solution for the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From the first equation: -5x + 7y = 67
Rearranging the equation: 7y = 5x + 67
Simplifying: y = (5/7)x + 67/7
Substituting this value for y in the second equation:
11x + 12((5/7)x + 67/7) = 17
11x + (60/7)x + 804/7 = 17
Multiplying through by 7 to get rid of the denominator: 77x + 60x + 804 = 119
Combining like terms: 137x + 804 = 119
Subtracting 804 from both sides: 137x = -685
Dividing by 137: x = -5
Substituting this value for x back into the equation for y:
y = (5/7)(-5) + 67/7
y = -25/7 + 67/7
y = 42/7
Simplifying: y = 6
Therefore, the solution for the system of equations is x = -5 and y = 6.