Use substitution to solve the following system of linear equations.4x+2y=74x+2y=7x+5y=4x+5y=4

(32,12)\left(\frac32,\frac12\right)

Use substitution to solve the following system of linear equations. 4 x + 2 y = 7 4x+2y=7 x + 5 y = 4 x+5y=4

everyone. So let's get started here. So we have this practice problem. We're gonna use the substitution method to solve the system of linear equations. We've got these two equations, 4x+2yequals7 and x+5yequals4. Wanna use the substitution method? Let's just go ahead and stick to the steps. The first one is I have to pick an equation, the easiest equation to isolate either x or y, and I wanna label that as equation a. So notice how I've got one of my equations over here that has lots of coefficients, 4x2y equals 7. If I wanna isolate x or y, I'm gonna have to do some extra work here. Whereas this equation already has x that's by itself without any coefficients, It's relatively easy to isolate. So this is gonna be my equation a, and that means the other one's gonna be equation b. So the the second thing I wanna do is actually wanna isolate that equation for a. So it's gonna be relatively simple. All I have to do is subtract 5 y from both sides, and I'll get that x is equal to negative 5 y+4. Alright? So now that I have an expression for, or x in in equation a, now I'm gonna move on to the 3rd step, which is I'm gonna take that equation and plug it into the other equation, which is equation b. Remember, equation b says that 4x+2yequals7, but instead of writing x, now I'm just gonna replace it with this, sort of the expression over that's over here. So we're gonna get 4 times this expression over here, which is negative 5 y+4, and I'm gonna add that to 2 y and it equals 7. Alright? Now if you actually take a look at this equation, we've gotten rid of all of the x's and all we have left are y's. Now all we have to do is just solve for b. Alright? This becomes a normal distribution problem. 4 times negative 5 y will become negative 20 y. 4 times, positive 4 becomes 16, and then we've got is plus 2 y over here, this equals 7. Alright? So if you sort of simplify this, what's gonna happen is that the negative 20 y and 2 y will combine to 18, so it'll be 18 y. And then we're gonna have we're gonna subtract 16 from both sides over here, and what you'll end up with is you'll end up with something like 9. Alright. So 7 minus 16 will give you 9. And so we go ahead and solve for this. What you're gonna get here is that y is equal to, once you divide by 18, you'll actually see that what you'll see is that this actually reduces to a fraction. 9 over 18 is really just 1 half, except there's a negative sign here, so don't forget that. So y is equal to negative 1 half. Alright? So that is the answer, for y. So that's one of the variables that I have. So that's basically all of step 3 over here. Now we just we just take this expression and we plug it back into either one of these two equations over here. Alright? So what I've got is I've got, I'm just gonna plug it back into equation b. Just gonna pick 1 at random. It'll work either way. And so if you plug this back into expression b, what you'll see is you get 4x+2y. But now what we do is this is 2 times negative one half, and this is gonna equal to 7. Alright? So if you'll notice here what happens is that now we solve for x now. So we have 2 times negative one half, this will actually just reduce to 2 f four x plus, this is 2 times negative one half, which actually just become negative one. So in other words, just 4 x minus 1 over here, this equals 7. Alright? Now we just sort of, now we just add 1 to both sides. We'll add one over here, and we'll end up with 4 x is equal to 8, and therefore, x is equal to 2. So that's my other answer, and that's really all there is to it. So I've got x equals 2, and I've got y equals negative one half. So again, you may see this written as a coordinate pair. You may see this written as 2 comma negative one half, but that is the answer to this system of equations. If you plug these two numbers back into these two expressions, you should get true statements for both of them. Alright? So this is what we did over here. This was the step 4 that we did. And I'm actually just gonna go ahead and skip step number 5. You can go ahead and pause the video, plug these two points back into these two equations, and you should see that you'll get true statements for both. Hopefully, that makes sense. Thanks for watching.

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Use substitution to solve the following system of linear equations.4x+2y=74x+2y=7x+5y=4x+5y=4

다음 시청

Use substitution to solve the following system of linear equations.
$4 x + 2 y = 7$
$x + 5 y = 4$