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GradeSolution of Linear Equations, Solution of Linear Equations

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How do you solve the system $2x - y = 8$ and $x + 2y = 9$

Solve $3(x + 6) + 2(x + 3) = 64$ for the value of $x$ .

How do you solve $\dfrac{{x - 3}}{4} + \dfrac{x}{2} = 3$ ?

Solve the following equation

$\dfrac{1}{2}x - 3 = 5 + \dfrac{1}{3}x$

$\dfrac{1}{2}x - 3 = 5 + \dfrac{1}{3}x$

Solve and check your answer: $\dfrac{2}{3}x + 3 = 11$

Solve the following simultaneous equations for $x\,and\,y$ :

$m(x + y) + n(x - y) - ({m^2} + mn + {n^2}) = 0$

$n(x + y) + m(x - y) - ({m^2} - mn + {n^2}) = 0$

(1) Let $x + y = a,x - y = b$ .

(2) Transfer the terms not containing $x\,and\,y$ to RHS.

(3) Add equations, substitute the value of $a\,and\,b$ and solve.

$m(x + y) + n(x - y) - ({m^2} + mn + {n^2}) = 0$

$n(x + y) + m(x - y) - ({m^2} - mn + {n^2}) = 0$

(1) Let $x + y = a,x - y = b$ .

(2) Transfer the terms not containing $x\,and\,y$ to RHS.

(3) Add equations, substitute the value of $a\,and\,b$ and solve.

Find the value of \[Q\] in the following system so that the solution to the system is \[\left\{ {\left( {x,y} \right):x - 3y = 4} \right\}\]?

\[x - 3y = 4\]

\[Qx - 6y = 8\]

\[x - 3y = 4\]

\[Qx - 6y = 8\]

Given the linear equation $2x + 3y - 8 = 0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is of intersecting lines:

(A) $2x + 3y + 9 = 0$

(B) $6x + 9y + 9 = 0$

(C) $3x + 2y + 9 = 0$

(D) None of these

(A) $2x + 3y + 9 = 0$

(B) $6x + 9y + 9 = 0$

(C) $3x + 2y + 9 = 0$

(D) None of these

Five years ago, the father was 7 times that of his son. At present time, the fatherâ€™s age is 4 times that of his son. Find the present age of son and father?

Solve the following systems of equations by the method of cross-multiplication:

5ax + 6by=28

3ax+ 4by=18

5ax + 6by=28

3ax+ 4by=18

Solve the following pair of equations graphically: \[x+y=4\], \[3x-2y=-3\]

Shade the region bounded by the lines representing the above equation and \[x-\]axis.

A. \[x=3,y=2\]

B. \[x=1,y=3\]

C. \[x=8,y=2\]

D. \[x=9,y=2\]

Shade the region bounded by the lines representing the above equation and \[x-\]axis.

A. \[x=3,y=2\]

B. \[x=1,y=3\]

C. \[x=8,y=2\]

D. \[x=9,y=2\]

How to solve the following equations?

$$1)5 + x = \dfrac{1}{2} - \dfrac{1}{3}$$,

$$2)\dfrac{1}{4} + x = \dfrac{1}{2} - \dfrac{1}{3}$$,

$$3)1 - \dfrac{1}{2} + m = \dfrac{3}{4} + \dfrac{1}{2}$$.

$$1)5 + x = \dfrac{1}{2} - \dfrac{1}{3}$$,

$$2)\dfrac{1}{4} + x = \dfrac{1}{2} - \dfrac{1}{3}$$,

$$3)1 - \dfrac{1}{2} + m = \dfrac{3}{4} + \dfrac{1}{2}$$.

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