Question

Solve the following using Substitution method 2x – 5y = -13 3x + 4y = 15

Answer 1

$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

• 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.

$2x-5y=-13, \: 3x+4y=15$

• Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

$2x-5y=-13$

• Add 5y to both sides of the equation.

$2x=5y-13$

• Divide both sides by 2.

$x=\frac{1}{2}\left(5y-13\right)$

• Multiply $\frac{1}{2}$ times 5y - 13.

$x=\frac{5}{2}y-\frac{13}{2}$

• Substitute $\frac{5y-13}{2}$ for x in the other equation, 3x + 4y = 15.

$3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15$

• Multiply 3 times $\frac{5y-13}{2}$.

$\frac{15}{2}y-\frac{39}{2}+4y=15$

• Add $\frac{15y}{2}$ to 4y.

$\frac{23}{2}y-\frac{39}{2}=15$

• Add $\frac{39}{2}$ to both sides of the equation.

$\frac{23}{2}y=\frac{69}{2}$

• Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

• Substitute 3 for y in $x=\frac{5}{2}y-\frac{13}{2}$. Because the resulting equation contains only one variable, you can solve for x directly.

$x=\frac{5}{2}\times 3-\frac{13}{2}$

• Multiply 5/2 times 3.

$x=\frac{15-13}{2}$

• Add $-\frac{13}{2}$ to $\frac{15}{2}$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

$\large\underline{ \underline{ \sf \: x=1 }}$

• The system is now solved. The value of x & y will be 1 & 3 respectively.

$\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}$