Example Question - solving simultaneous equations
Here are examples of questions we've helped users solve.
Solving Simultaneous Equations by Elimination Method
To solve the system of simultaneous equations: 2x - 5y = 4 ...(1) 3x + 2y = -13 ...(2) We can use either the substitution method or the elimination method. Here, I will use the elimination method. First, let's try to eliminate one of the variables by making the coefficients of either x or y the same in both equations. If we multiply equation (1) by 3 and equation (2) by 2, we will get the coefficients of x to be the same: 3*(2x - 5y) = 3*4 2*(3x + 2y) = 2*(-13) This results in: 6x - 15y = 12 ...(3) 6x + 4y = -26 ...(4) Now, we will subtract equation (4) from equation (3) to eliminate x and find y: (6x - 15y) - (6x + 4y) = 12 - (-26) 6x - 6x - 15y - 4y = 12 + 26 -19y = 38 Divide both sides by -19 to find y: y = 38 / -19 y = -2 Now we know the value of y; we can substitute it into either original equation (1) or (2) to find x. We'll use equation (1): 2x - 5*(-2) = 4 2x + 10 = 4 Subtract 10 from both sides: 2x = 4 - 10 2x = -6 Divide by 2 to solve for x: x = -6 / 2 x = -3 So the solution to the system of equations is: x = -3 y = -2
Solving Simultaneous Equations with Undetermined System
The image displays a set of simultaneous equations to be solved. However, the quality of the image, with blurred text, makes it difficult to provide accurate assistance. Despite the low resolution, I will attempt to interpret the equations and solve one of them based on what can be reasonably discerned: It seems that "a" is the selected equation pair to solve: a) \( \begin{cases} 2x - y = 4z \\ z + t = -3y + 5 \end{cases} \) To solve this system of equations, we would likely need more information or additional equations involving all variables \( x, y, z, \) and \( t \) to provide a unique solution. With only two equations and four unknowns, the system is underdetermined. This means there are an infinite number of solutions that can satisfy both equations, depending on the values of two of the variables, which can be chosen freely. If you can provide clearer images or more context, I can give a more precise answer on how to approach solving these equations.
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