Example Question - opposite coefficients
Here are examples of questions we've helped users solve.
Solving Equations with Elimination of Variables
To solve for x, we have these two equations from the image without the y variables: 1) -2x + 4y = 15 2) -12x - 4y = -8 Adding these two equations together will eliminate the y terms since they have opposite coefficients: -2x + 4y = 15 -12x - 4y = -8 ---------------- -14x = 7 Now, we solve for x by dividing both sides of this equation by -14: -14x / -14 = 7 / -14 x = -1/2 Therefore, the value of x is -1/2, which corresponds to option A: -1/2.
Solving a System of Equations by Addition Method
The system of equations provided is: -5x - 6y = -2 4x + 6y = -2 This 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 = -4 So we have: -x = -4 Dividing both sides by -1 to solve for x: x = 4 Now 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 = -2 Substitute x = 4: -5(4) - 6y = -2 -20 - 6y = -2 Add 20 to both sides to isolate terms with y: -6y = -2 + 20 -6y = 18 Divide both sides by -6 to solve for y: y = 18 / -6 y = -3 The solution to the system of equations is: x = 4 y = -3
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