Solve the above set of equations and choose the correct answer.$$ (I)-5x+4y=3 $$$$ (II)6x-8y=10 $$

$$ x=-4,y=-4\frac{1}{4} $$

$$ x=-4,y=4\frac{1}{4} $$

$$ x=-4\frac{1}{4},y=4 $$

$$ x=-4,y=-4\frac{1}{4} $$

Find the value of x and and band the substitution method.$$ (I)-x+3and=12 $$$$ (II)4x+2and=10 $$

$$ x=\frac{3}{7},y=\frac{29}{7} $$

$$ x=\frac{4}{9},y=\frac{5}{9} $$

Solve the above set of equations and choose the correct answer.$$ (I)\frac{1}{3}x-4y=5 $$$$ (II)x+6y=9 $$

$$ x=11,y=-\frac{1}{3} $$

$$ x=-11,y=-\frac{1}{3} $$

$$ x=-\frac{1}{3},y=-11 $$

$$ x=\frac{1}{3},y=-11 $$

$$ x=11,y=-\frac{1}{3} $$

Find the value of x and and band the substitution method.$$ (I)-4x+4and=15 $$$$ (II)2x+8and=12 $$

$$ x=-\frac{9}{5},y=\frac{39}{20} $$

$$ x=\frac{5}{13},y=-\frac{8}{13} $$

$$ x=-\frac{9}{5},y=\frac{39}{20} $$

Substitution method for two linear equations with two unknowns

To solve with the substitution method a system of two linear equations with two unknowns we will have to substitute one of the unknowns in some equation and thus obtain an equation with only one unknown.

How do we do it?

Choose the equation in which you can easily isolate one of the unknowns (isolate it in such a way that it cannot express itself).
Put the unknown that you have isolated in the second equation of the system: you will have an equation with one unknown and you will discover the value of the first one.
Go back to the system of equations and place the value of the unknown you found in one of the equations or in the equation obtained to find the second unknown.

Detailed explanation

Start practice

Test yourself on algebraic solution!

Solve the following equations:

$$ (I)x+y=18 $$

$$ (II)y=13 $$

Practice more now

Example of the substitution method

$X+2Y=20$
$4X-3Y=14$

Let's isolate the $X$ from the first equation since it is the easiest:
$X=20-2Y$
Let's substitute the $X$ in the second equation:
$4\times (20-2y)-3y=14$
We obtained an equation with one unknown, therefore, we will solve it easily:
$80-8y-3y=14$
$80-11y=14$
$-11y=-66$
$y=6$

Let's place the value obtained in the simpler equation (the equation we obtained after isolating the $X$ ) and find the second unknown:
$x=20-2\times 6$
$x=8$
The solution is: $x=8$
$y=6$

If you are interested in this article you may also be interested in the following articles

Unknowns and Algebraic Expressions
First-degree equations with an unknown variable
What is the unknown of a mathematical equation?
System of Two Linear Equations with Two Unknowns
Linear equation with two unknowns
Graphical solution for a system of linear equations with two unknowns
Algebraic solution for a system of linear equations with two unknowns
Solving by the method of substitution for systems of two linear equations with two unknowns
Solving verbal problems with a system of linear equations

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