How to Simultaneous Equation using substitution method

Question: Find the values of  x and y in the equations below

3x+2y=6

5x−y=8

Solution

Using substitution method

3x+2y=6

5x−y=8

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation

3x+2y=6,5x−y=8

Choose one of the equations and solve it for $x$ by isolating $x$ on the left hand side of the equal sign.

3x+2y=6

Subtract $2y$ from both sides of the equation.

3x=−2y+6

Divide both sides by $3$.

x=31​(−2y+6)

Multiply $\frac{1}{3}$ times $-2y+6$.

x=−32​y+2

Substitute $-\frac{2y}{3}+2$ for $x$ in the other equation, $5x-y=8$.

5(−32​y+2)−y=8

Multiply $5$ times $-\frac{2y}{3}+2$.

−310​y+10−y=8

Add $-\frac{10y}{3}$ to $-y$

−313​y+10=8

Subtract $10$ from both sides of the equation.

−313​y=−2

Divide both sides of the equation by $-\frac{13}{3}$, which is the same as multiplying both sides by the reciprocal of the fraction.

y=136

Substitute $\frac{6}{13}$ for $y$ in $x=-\frac{2}{3}y+2$. Because the resulting equation contains only one variable, you can solve for $x$ directly.

x=−32​×(136​)+2

Multiply $-\frac{2}{3}$ times $\frac{6}{13}$ by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

x=−134​+2

Add $2$ to $-\frac{4}{13}$.

 x=
13
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