3x-2y=14 2x-3y=11 solve algebraically

The value of x is 4 and y is -1.

Given that,

Equation; 3x - 2y = 14, 2x - 3y = 11

We have to solve

the solution of the equation.

According to the question,

The solution of the equation finding by using elimination method following all the steps given below.

From equation 1,

Substitute the value of x in equation 2,

Again, substitute the value of x in equation 1,

Hence, The value of x is 4 and y is -1.

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x = 4, y = - 1

Step-by-step explanation:

The given system of simultaneous equations is expressed as

3x - 2y = 14 - - - - - - - - - - - - 1

2x - 3y = 11- - - - - - - - - - - - - 2

The first step is to decide on which variable to eliminate. Let us eliminate x. Then we would multiply both rows by numbers which would make the coefficients of x to be equal in both rows.

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x - 4y = 28

6x - 9y = 33

Subtracting, it becomes

5y = - 5

y = - 5/- 5 = - 1

The next step is to substitute y = - 1 into any of the equations to determine x.

Substituting y = - 1 into equation 2, it becomes

2x - 3 × - 1 = 11

2x + 3 = 11

2x = 11 - 3 = 8

x = 8/2

x = 4

1010: 3030

is it i think

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.