Question - Solving a System of Equations by Addition Method
Solution:
The system of equations provided is:-5x - 6y = -24x + 6y = -2This system can be solved by adding the two equations together, as the y terms will cancel each other out given they have opposite coefficients.Adding the left sides of the equations:-5x - 6y + 4x + 6y = -2 + (-2)Combining like terms:-5x + 4x = -x-6y + 6y = 0-2 - 2 = -4So we have:-x = -4Dividing both sides by -1 to solve for x:x = 4Now that we have a value for x, we can substitute this value into either one of the original equations to find the value of y. Let's use the first equation:-5x - 6y = -2Substitute x = 4:-5(4) - 6y = -2-20 - 6y = -2Add 20 to both sides to isolate terms with y:-6y = -2 + 20-6y = 18Divide both sides by -6 to solve for y:y = 18 / -6y = -3The solution to the system of equations is:x = 4y = -3
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