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

Question

asked Mar 13, 2022 70.2k views

1 Answer

Bill · Answer 1 · 2022-03-18T02:49:33+0000

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

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

2x=5y-13

$x=(1)/(2)\left(5y-13\right) \\$

$x=(5)/(2)y-(13)/(2) \\$

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

$(15)/(2)y-(39)/(2)+4y=15 \\$

$(23)/(2)y-(39)/(2)=15 \\$

$(23)/(2)y=(69)/(2) \\$

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
$x=(5)/(2)y-(13)/(2)\\$ . Because the resulting equation contains only one variable, you can solve for x directly.

$x=(5)/(2)* 3-(13)/(2) \\$

$x=(15-13)/(2) \\$

Add
$-(13)/(2)\\$ to
$(15)/(2)\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

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

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