Question - Solving Simultaneous Equations by Elimination Method
mathsystem of equationselimination methodsubstitution methodcoefficientssolving simultaneous equations
Solution:
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*42*(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 = 38Divide both sides by -19 to find y:y = 38 / -19y = -2Now 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) = 42x + 10 = 4Subtract 10 from both sides:2x = 4 - 102x = -6Divide by 2 to solve for x:x = -6 / 2x = -3So the solution to the system of equations is:x = -3y = -2
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