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How do u solve this symultanious equation

5x-2y=8
3x+3y=9​

User Valvoline
by
8.5k points

1 Answer

4 votes

STEPS USING SUBSTITUTION

5x−2y=17

2x−3y=9

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.

5x−2y=17,2x−3y=9

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

5x−2y=17

Add 2y to both sides of the equation.

5x=2y+17

Divide both sides by 5.

x=

5

1

(2y+17)

Multiply

5

1

times 2y+17.

x=

5

2

y+

5

17

Substitute

5

2y+17

for x in the other equation, 2x−3y=9.

2(

5

2

y+

5

17

)−3y=9

Multiply 2 times

5

2y+17

.

5

4

y+

5

34

−3y=9

Add

5

4y

to −3y.

5

11

y+

5

34

=9

Subtract

5

34

from both sides of the equation.

5

11

y=

5

11

Divide both sides of the equation by −

5

11

, which is the same as multiplying both sides by the reciprocal of the fraction.

y=−1

Substitute −1 for y in x=

5

2

y+

5

17

. Because the resulting equation contains only one variable, you can solve for x directly.

x=

5

2

(−1)+

5

17

Multiply

5

2

times −1.

x=

5

−2+17

Add

5 /17

​ to −

5 /2

​ by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

x=3

The system is now solved.

x=3,y=−1

User Emkman
by
8.0k points

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