**Solve each equation. Check your solution.**

In particular, we can set each of the factors equal to zero, and solve the resulting equation for one solution of the original equation. We can only draw the helpful conclusion about the factors (namely, that one of those factors must have been equal to zero, so we can set the factors equal to zero) if the product itself equals zero. If the product of factors is equal to anything non-zero... Key Steps in Solving Exponential Equations without Logarithms. Make the base on both sides of the equation the SAME. so that if b M = b N. then M = N. For more math videos, click "VIDEOS" on the menu above. In other words, if you can express the exponential equations to have the same base on both sides then it’s OKAY to set their powers or exponents equal to each other. You should also

**SOLUTION Solve each system of equations x+2y=12 3y-4z=25**

This solution demonstrates the logical basis for how this entire class of equation is solved: If the bases are the same, then the powers must also be equal; this is the only way for the two sides of the equation to be equal to each other....In such cases, we have to solve the equation by completing the square, or using the quadratic formula (see below). In order to complete the square, we need to rewrite the given equation in the form ( x + a ) 2 = b {\displaystyle (x+a)^{2}=b} .

**Solve each equation. Check your solution.**

We obtained Equation (2) by adding the same quantity, -2x, to each member of Equation (1), in that way getting y by itself. In general, we can write equivalent equations in two variables by using the properties we introduced in Chapter 3, where we solved first-degree equations in one variable. how to stay top of your class In such cases, we have to solve the equation by completing the square, or using the quadratic formula (see below). In order to complete the square, we need to rewrite the given equation in the form ( x + a ) 2 = b {\displaystyle (x+a)^{2}=b} .. How to solve distance and displacement

## How To Solve Each Equation

### Solve each equation. Check your solution.

- SOLUTION Solve each system of equations x+2y=12 3y-4z=25
- Solve each equation. Check your solution.
- Solve each equation. Check your solution.
- SOLUTION Solve each system of equations x+2y=12 3y-4z=25

## How To Solve Each Equation

### Key Steps in Solving Exponential Equations without Logarithms. Make the base on both sides of the equation the SAME. so that if b M = b N. then M = N. For more math videos, click "VIDEOS" on the menu above. In other words, if you can express the exponential equations to have the same base on both sides then it’s OKAY to set their powers or exponents equal to each other. You should also

- Solving linear equations with one variable Linear equations in one variable are equations where the variable has an exponent of 1, which is typically not shown (it is understood). An example would be something like \(12x = x – 5\).
- Multiply each term in the first equation by –2 (you get –2x – 6y = –8) and then add the terms in the two equations together. You choose the number –2 as a multiplier because it makes the coefficient of the x term in the first equation equal to –2, while the coefficient on x in the second equation is 2.
- Solve the following pair of simultaneous linear equations: Equation 1: 2x + 3y = 8 Equation 2: 3x + 2y = 7 Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient. An easy choice is to multiply Equation 1 by 3, the
- In such cases, we have to solve the equation by completing the square, or using the quadratic formula (see below). In order to complete the square, we need to rewrite the given equation in the form ( x + a ) 2 = b {\displaystyle (x+a)^{2}=b} .

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