Solving systems of equations quiz part 2
1. Solve the system of equations:
x + 2y = 7
3x - y = 3
Solution:
From the first equation, we can isolate x by subtracting 2y from both sides:
x = 7 - 2y
Substituting this expression for x into the second equation, we get:
3(7 - 2y) - y = 3
Simplifying this equation, we get:
21 - 7y - y = 3
-8y = -18
y = 2.25
Now, to find x, we can substitute this value of y into either of the original equations. Let's use the first one:
x + 2(2.25) = 7
x + 4.5 = 7
x = 2.5
So the solution to the system of equations is (x, y) = (2.5, 2.25).
2. Solve the system of equations:
2x - 3y = -5
4x + y = 19
Solution:
Let's first isolate y in the first equation:
-3y = -2x - 5
y = (2/3)x + (5/3)
Now we can substitute this expression for y into the second equation:
4x + (2/3)x + (5/3) = 19
Multiplying both sides by 3 to get rid of the fraction, we get:
12x + 2x + 5 = 57
14x = 52
x = 3.714
Finally, we can substitute this value of x into either of the expressions for y. Let's use the first one:
2(3.714) - 3y = -5
7.428 - 3y = -5
-3y = -12.428
y = 4.143
So the solution to the system of equations is (x, y) = (3.714, 4.143).