3.
y = 2x - 5
4x - y = 7
Add y to both sides in 2nd equation.
4x = 7 + y
Subtract 7 from both sides.
4x - 7 = y
Now that both equations are set equal to y, we can set them equal to each-other to quickly solve for x.
2x - 5 = 4x - 7
Subtract 2x from both sides.
-5 = 2x - 7
Add 7 to both sides.
2 = 2x
Divide both sides by 2.
x = 1
The value of x is 1, and so we can find the value of y.
y = 4x - 7
y = 4(1) - 7
y = 4 - 7
y = -3
The value of y is -3.
The value of x is 1.
4.
2x - 3y = 12
x = 4y + 1
Because we have a value of x, we can plug it into the first equation to solve for y.
2(4y + 1) - 3y = 12
Distributive property.
8y + 2 - 3y = 12
Combine like terms.
5y + 2 = 12
Subtract 2 from both sides.
5y = 10
Divide both sides by 5.
y = 2.
Now that we have a value for y we can solve for x.
x = 4y + 1
x = 4(2) + 1
x = 8 + 1
x = 9
The value of y is equal to 2.
The value of x is equal to 9.
I hope this helps!