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What is the solution of the system?
y = 3x - 10
3x + 2y = 16

User Tim Ward
by
7.8k points

1 Answer

4 votes
We can solve this system of equations using substitution or elimination method.

Method 1: Substitution Method
In this method, we solve one equation for one variable and substitute the expression in the other equation.

From the first equation, we get y = 3x - 10.

Substituting y in the second equation, we get:

3x + 2(3x - 10) = 16
3x + 6x - 20 = 16
9x = 36
x = 4

Substituting x in the first equation, we get:

y = 3(4) - 10
y = 2

Therefore, the solution of the system is (4, 2).

Method 2: Elimination Method
In this method, we multiply one or both equations by a constant such that one variable gets eliminated when we add or subtract the equations.

Multiplying the first equation by 2, we get:

2y = 6x - 20

Subtracting the above equation from the second equation, we get:

3x + 2y - 2y = 16 - (-20)
3x = 36
x = 4

Substituting x in the first equation, we get:

y = 3(4) - 10
y = 2

Therefore, the solution of the system is (4, 2).
User Aracelis
by
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