Solve Systems of Linear Equations Calculator Which ordered pair is the solution to this system of equations?
x=(1)/(2)y+5
2x+3y=-14
Final answer:
To solve the given system of linear equations, we can use the substitution method. By substituting the value of x into equation (2), we can solve for y. Substituting the value of y back into equation (1), we can solve for x. The solution to the system of equations is the ordered pair (2, -6).
Explanation:
To solve the given system of linear equations:
x = (1/2)y + 5 (1)
2x + 3y = -14 (2)
We can solve this system by substitution or elimination. Let’s use the substitution method.
From equation (1), we can express x in terms of y: x = (1/2)y + 5.
Substituting this value of x into equation (2), we get:
2((1/2)y + 5) + 3y = -14
Simplifying:
y + 10 + 3y = -14
4y + 10 = -14
4y = -24
y = -6
Substituting this value of y back into equation (1), we can solve for x:
x = (1/2)(-6) + 5
x = -3 + 5
x = 2
Therefore, the solution to the system of equations is the ordered pair (2, -6).
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