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22 votes
22 votes
{ 4x−3y=12

7x−3y=3
Solve the system of equations using the linear combination method.
x=
y=

User Monis Majeed
by
2.4k points

1 Answer

21 votes
21 votes

Answer:

x= -3

y= -8

Explanation:

- 4x−3y=12,7x−3y=3

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.

-

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

4x−3y=12

Add 3y to both sides of the equation.

4x=3y+12

Divide both sides by 4.

x = 1\4(3y+12)

Multiply 1\4 times 12+3y.

x = 3\4y + 3

-

Substitute 3y\4 + 3

for x in the other equation, 7x−3y=3.

7( 3\4y + 3 ) - 3y = 3

Multiply 7 times 3y\4 + 3

21\4y + 21 -3y = 3

Add 21y\4 to -3y

-

9\4y = -18

Divide both sides of the equation by 9\4 which is the same as multiplying both sides by the reciprocal of the fraction.

y = −8

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Substitute −8 for y in x = 3\4y + 3. Because the resulting equation contains only one variable, you can solve for x directly.

x = 3\4(-8)+3

Multiply 3\4 times -8

x=−6+3

Add 3 to −6.

x = −3

User LeZuse
by
3.3k points