porttoyou.blogg.se - Solve by substitution

#Solve by substitution plus#

Half an hour later, Tina left Riverside in her car on the same route as Stephanie, driving 70 miles per hour. Stephanie left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 56 miles per hour. How many stoves would Mitchell need to sell for the options to be equal?

#Solve by substitution plus#

Company B offers him a position with a salary of $24,000 plus a $50 commission for each stove he sells.

Mitchell currently sells stoves for company A at a salary of $12,000 plus a $150 commission for each stove he sells.

How many cable packages would need to be sold to make the total pay the same? The second pays a salary of $20,000 plus a commission of $25 for each cable package sold. The first company pays a salary of $ 14,000 plus a commission of $100 for each cable package sold.

Jackie has been offered positions by two cable companies.

The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle.

The measure of one of the small angles of a right triangle is 26 more than 3 times the measure of the other small angle.

The length is 10 more than three times the width. In the following exercises, translate to a system of equations and solve. In the following exercises, solve the systems of equations by substitution.

Check that the ordered pair is a solution to both original equations.

Substitute the solution in Step 3 into one of the original equations to find the other variable.

Substitute the expression from Step 1 into the other equation.

Solve one of the equations for either variable.

Solve a system of equations by substitution.

Instructional Video-Solve by Substitution.

Instructional Video-Solve Linear Systems by Substitution.

Even if your textbook didn’t ask you to check your work it’s always a good idea to do this process, it only takes about a minute maybe less and that way you’re going to make sure you get A pluses on your homework and also on your tests. That’s how I know I did this problem correctly.

My y quantity I hope is equal to 2 times my x quantity take away 3.

I also need to check it into the second equation. Good so I’m half way there, I think it's right. So here comes my check, first I’m going to check it in the first equation, is it true that my y quantity is equal to 3 times my x quantity plus 1? Let’s see -11 equals -12 plus 1, yap that’s true. In order to check my work, I’m going to go back and plug in -4 for x and -11 to y into both original equations and make sure I get equalities. I’m pretty sure that’s my answer, I’m pretty sure that’s the point where these lines cross even though I didn’t graph them. Y is equal to 3 times my x quantity plus 1, so y is equal to -11 oops, that’s a +1 right there, plus 1 okay. I could also use the second one and I’ll still get the same answer for y. I’m just going to choose to use the first equation. In order to find y, I’m going to take x equals -4, and substitute it into either original equation, that way I’ll get my y value, and I’ll go back and check in a second. I’m going to put a box around this like I would have with my whole answer keeping in mind I still need to find what that y value is. Keep in mind that’s only going to be half of my answer. Now I need to get x all by itself by subtracting 1 from both sides, x is equal to -4. Here we go if I want to find x, I’m going to subtract 2 Xs from both sides, so now I have x plus 1 equals -3. I’m going to find x, and then go back and find my y value. Now this is a straight forward solving problem. Just as when solving integrals, one method to try is to change variables to end up with a simpler equation to solve. That guy is equal to y and that guy is also equal to y, so I’m just substituting those two equations so they look like one equation with one variable. Since I know y is equal to the expression 3x plus 1, and y is also equal to the expression 2x minus 3, it makes sense mathematically to write 3x plus 1 equals 2x minus 3. This problem using substitution is going to be not too difficult because I have 2 equations that are both already solved for y.