To answer this, I'll use an example:
Say you're equations are both in slope-intercept form:
y = 3x + 5
y = x + 7
You substitute one equation into another (since y = y, you can set it up in the same equation).
x + 7 = 3x + 5
Subtract variables.
7 = 2x +5
Subtract numbers.
2 = 2x
Divide.
1 = x
You could also have a problem with one or two standard form equations. First, make sure you have at least one slope-intercept equation. Here's an example:
3x - 2y = 20
y = x + 15
Substitute the slope-intercept equation into y (because y = y).
3x - 2(x + 15) = 20
Distribute.
3x- 2x - 30 = 20
Like terms!
x - 30 = 20
Add 30 to both sides.
x = 50
For both equations, you can substitute your solution into one of the equations to find the other variable.
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Gaussian elimination is used to solve systems of linear equations.
Linear transformations can be very important in graphics. Also, linear transformations come up whenever you need to solve systems of linear equations, which arise quite often. Finally, they can be useful in further areas of mathematics such as topology.
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
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If you are trying to solve a linear equation and facing difficulty in doing so then try to understand that the variable which u have taken is depending on what factor..and equate it with the constant..by doing this you will be able to solve the equation.