To solve this system of equations, we can use the method of substitution or elimination.
1. Substitution method:
From the first equation, we can solve for x in terms of y:
x = 5y + 7
Substitute this expression for x into the second equation:
3(5y + 7) - 2y = -4
15y + 21 - 2y = -4
13y + 21 = -4
13y = -25
y = -25/13
Now, substitute the value of y back into the first equation to solve for x:
x = 5(-25/13) + 7
x = -125/13 + 91/13
x = -34/13
Therefore, the solution to the system of equations is x = -34/13 and y = -25/13.
2. Elimination method:
To use the elimination method, we can multiply the first equation by 2 and the second equation by 5 to make the coefficients of y in both equations the same:
2(x - 5y) = 2(7) -> 2x - 10y = 14
5(3x - 2y) = 5(-4) -> 15x - 10y = -20
Subtract the first equation from the second equation to eliminate y:
15x - 10y - (2x - 10y) = -20 - 14
13x = -34
x = -34/13
Now, substitute the value of x back into the first equation to solve for y:
x - 5y = 7
-34/13 - 5y = 7
-5y = 7 + 34/13
-5y = 91/13
y = -25/13
Therefore, we get the same solution as before: x = -34/13 and y = -25/13.
Previously graph of a system of two linear equation in two variables: x -5y = 7 and 3x - 2y = -4.
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