How to solve linear equations by substitution?

Given the equations:
1. \(5x + 2y = 9\)
2. \(x + y = -3\)

5x+2y=9 x+y=3
change x+y=3 into x=3-y
plug that equation into 5x+2y=9 where x is.
5(3-y)+2y=9
then distribute.
15-5y+2y=9
15-7y=9
minus 15.
-7y=-6
divide both sides by -7.
y is equal to -6/7.
then go back to the first equation and plug in for y.
and then you will get x.
then you will have (y,x)

Answered by krissyjoy | 2024-06-10

{ 5 x + 2 y = 9 x + y = − 3 ​ { 5 x + 2 ∗ ( − 3 − x ) = 9 y = − 3 − x ​ { 5 x − 6 − 2 x = 9 y = − 3 − x ​ { 3 x = 9 + 6 y = − 3 − x ​
{ 3 x = 15 / : 3 y = − 3 − x ​ { x = 5 y = − 3 − 5 ​ { x = 5 y = − 8 ​

Answered by Lilith | 2024-06-10

To solve the system of equations 5 x + 2 y = 9 and x + y = − 3 using substitution, we express x from the second equation, substitute it into the first equation, and solve for y . Once y is found, we substitute it back to find x . The solution is ( 5 , − 8 ) .
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Answered by krissyjoy | 2024-12-23