MP Board · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesSolve the following system of linear equations using the method of substitution.

Method of Substitution \nThe method of substitution is one of the methods used to solve a system of linear equations. This method involves solving one of the equations for one variable and then substituting that expression into the other equation.

Step 1: Solve one of the equations for one variable.\nLet's solve the first equation for x. We have:

2x + 3y = 7 \nSubtracting 3y from both sides gives us:

2x = 7 - 3y \nDividing both sides by 2 gives us: \nx = (7 - 3y) / 2

Step 2: Substitute the expression for x into the other equation.\nNow that we have an expression for x, we can substitute it into the second equation. We have: \nx + 2y = 4 \nSubstituting x = (7 - 3y) / 2 into this equation gives us:

((7 - 3y) / 2) + 2y = 4 \nMultiplying both sides by 2 to eliminate the fraction gives us:

7 - 3y + 4y = 8 \nSimplifying this equation gives us: \ny = 1

Step 3: Find the value of x.\nNow that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation. We have:

2x + 3y = 7 \nSubstituting y = 1 into this equation gives us:

2x + 3(1) = 7 \nSimplifying this equation gives us:

2x + 3 = 7 \nSubtracting 3 from both sides gives us:

2x = 4 \nDividing both sides by 2 gives us: \nx = 2 \nTherefore, the solution to the system of linear equations is x = 2 and y = 1.