The solution to the system of equations is x = 8/17 and y = 61/17.
By verifying the solution by substitution, 5 = 5 and -12 = -12 implying that the two equations are satisficed.
Mia's method of eliminating x by multiplying the first equation by 3 and the second equation by 2 will work
Eliminating y directly might be simpler in this case because the coefficient of y in the second equation is already -1.
The solution to Mia's system of equations is x = -1 and y = 3.
How to solve the system of equations algebraically
To solve the system of equations algebraically:
Solve the first equation for y:
3x + y = 5
y = 5 - 3x
Substitute the value of y in the second equation:
5x - 4(5 - 3x) = -12
5x - 20 + 12x = -12
17x - 20 = -12
17x = 8
x = 8 / 17
Substitute the value of x back into the first equation to find y:
3(8 / 17) + y = 5
24 / 17 + y = 5
y = 5 - 24 / 17
y = (85 - 24) / 17
y = 61 / 17
Therefore, the solution to the system of equations is x = 8/17 and y = 61/17.
To verify the solution algebraically using substitution:
Substitute the values of x and y into the original equations:
For the first equation:
3x + y = 5
3(8/17) + 61/17 = 5
24/17 + 61/17 = 5
85/17 = 5
5 = 5
For the second equation:
5x - 4y = -12
5(8/17) - 4(61/17) = -12
40/17 - 244/17 = -12
-204/17 = -12
-12 = -12
Both equations are satisfied by the values of x = 8/17 and y = 61/17.
Therefore, the solution is verified algebraically using substitution.
Mia's method of eliminating x by multiplying the first equation by 3 and the second equation by 2 will effectively eliminate x when the equations are added together.
However, eliminating y directly might be simpler in this case because the coefficient of y in the second equation is already -1, making it easier to eliminate y by adding the equations together without prior multiplication.
The original system of equations is:
2x + 3y = 7
3x - y = -6
To solve Mia system of equation
Multiply the first equation by 3, we have
6x + 9y = 21
multiply the second equation by 2, we get
6x - 2y = -12.
Now, subtract the second equation from the first equation, the x variable will be eliminated:
(6x + 9y) - (6x - 2y) = 21 - (-12)
6x + 9y - 6x + 2y = 21 + 12
11y = 33
Divide both sides of the equation by 11
y = 3.
Now, substitute this value of y back into one of the original equations. Let's use the first equation,
2x + 3y = 7:
2x + 3(3) = 7
2x + 9 = 7
2x = 7 - 9
2x = -2
x = -1
Thus, the solution to Mia's system of equations is x = -1 and y = 3.