Algebra: linear equations

Content Level-1 Problem-192 Click for video

Steps	Problem	Solution
1	Simplify the expressions by using subtraction	\$ (1/2x^2+2/3y^2+1/3xy)-(4/5x^2-1/4y^2+1/5xy) \$
2	Given expressions	\$ (1/2x^2+2/3y^2+1/3xy)-(4/5x^2-1/4y^2+1/5xy) \$
3	After eleminating the brackets we get	\$ 1/2x^2+2/3y^2+1/3xy - 4/5x^2+1/4y^2-1/5xy \$
4	Grouping like terms together	\$ 1/2x^2-4/5x^2+2/3y^2+1/4y^2+1/3xy-1/5xy \$
5	Taking common factor from the like terms after we write	\$ (1/2-4/5)x^2 +(2/3+1/4)y^2 +(1/3 -1/5)xy \$
6	Find the lcm for the denominators	\$ (5-8)/10x^2+(8+3)/12y^2+(5-3)/15xy \$
7	After simplification we get	\$ -3/10x^2+11/12y^2+2/15xy \$
8	Hence the solution of the given expressions ares	\$ (-3x^2)/10+(11y^2)/12+(2xy)/15 \$

Steps

Problem

Solution

Simplify the expressions
by using subtraction

\$ (1/2x^2+2/3y^2+1/3xy)-(4/5x^2-1/4y^2+1/5xy) \$

Given expressions

\$ (1/2x^2+2/3y^2+1/3xy)-(4/5x^2-1/4y^2+1/5xy) \$

After eleminating the brackets we get

\$ 1/2x^2+2/3y^2+1/3xy - 4/5x^2+1/4y^2-1/5xy \$

Grouping like terms together

\$ 1/2x^2-4/5x^2+2/3y^2+1/4y^2+1/3xy-1/5xy \$

Taking common factor from the like terms
after we write

\$ (1/2-4/5)x^2 +(2/3+1/4)y^2 +(1/3 -1/5)xy \$

Find the lcm for the denominators

\$ (5-8)/10x^2+(8+3)/12y^2+(5-3)/15xy \$

After simplification we get

\$ -3/10x^2+11/12y^2+2/15xy \$

Hence the solution of the given expressions ares

\$ (-3x^2)/10+(11y^2)/12+(2xy)/15 \$