Find the solution of the system of equations. {:[4x+6y=16],[3x-2y=25]:}

Question

Find the solution of the system of equations.  {:[4x+6y=16],[3x-2y=25]:}

Bytelearn · Accepted Answer

Elimination Method: Let's start by solving the system of equations using the method of substitution or elimination. We will use the elimination method to eliminate one of the variables. First, we need to make the coefficients of one of the variables the same in both equations. We can do this by multiplying the second equation by 3 to match the coefficient of y in the first equation.New System of Equations: Multiply the second equation by 3 to get a new system of equations where the coefficients of y are the same: 4x + 6y = 16 (Equation 1) 9x - 6y = 75 (Equation 2 multiplied by 3)Eliminate y: Now, add Equation 1 and Equation 2 to eliminate y: (4x + 6y) + (9x - 6y) = 16 + 75 This simplifies to: 4x + 9x = 91Solve for x: Combine like terms to solve for x: 13x = 91 Divide both sides by 13 to find the value of x: x = 91 / 13 x = 7Substitute x into Equation: Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use Equation 1: 4x + 6y = 16 Substitute x = 7 into Equation 1: 4(7) + 6y = 16Solve for y: Perform the multiplication: 28 + 6y = 16 Subtract 28 from both sides to solve for y: 6y = 16 - 28 6y = -12 Divide both sides by 6 to find the value of y: y = -12 / 6 y = -2

Find the solution of the system of equations. $\newline$ $\begin{array}{l} 4 x+6 y=16 \\ 3 x-2 y=25 \end{array}$

Full solution

More problems from Write an equation word problem

Related topics

Find the solution of the system of equations.\newline4x+6y=163x−2y=25 \begin{array}{l} 4 x+6 y=16 \\ 3 x-2 y=25 \end{array} 4x+6y=163x−2y=25​

Find the solution of the system of equations. $\newline$ $\begin{array}{l} 4 x+6 y=16 \\ 3 x-2 y=25 \end{array}$