Given the equation 2 x + 3 y = 10 2x+3y=10 what is the missing variable shown below? (__, − 5 3 -\frac53 )

Here we are given the equation two x plus three y equals 10, and we want to know what is the missing variable shown below. Now I have this ordered pair in the form x y, and I can see that my y is given to me. So it's really the x that I'm looking for. But that's fine, because I can see we have x in this equation and y. So I can just plug in my y, solve for x, and that will give me the solution. So we have two x plus three times y. Now rather than plugging in y, I'm going to plug in the variable that I'm given in my ordered pair, negative five over three. And then all of this is going to be equal to 10. Now from here, x is the only unknown, so I just need to use my algebra skills to solve for x. Now what I'm going to do is cancel the three's, because I can do that since it's in the numerator and it's or since it's being multiplied and it's in the denominator, those will cancel, leaving me with 2x plus negative five, which I can also write is just minus five, is equal to 10. Now from here I'm going to add five on both sides of this equal sign, getting the fives to cancel right about there. So what we end up getting is two x is equal to 10 plus five, which is 15. Now from here, I can go ahead and divide two on both sides of the equal sign. That's going to get the twos to cancel right about here, giving me that x is equal to 15 over two. Now, this does not reduce any farther, so 15 over two is going to be our answer as a reduced fraction, so that means that 15 over two, and I'm gonna write it like this actually. Actually, no. No. I'm gonna write it as 15 over two. We'll put this in the blank right about here, just to avoid confusion. So this is going to be my ordered pair and the solution to this problem. Hope you found this video helpful.

8. Graphing and Introduction to Statistics

Graph Linear Equations in Two Variables

Prealgebra

8. Graphing and Introduction to Statistics

Graph Linear Equations in Two Variables

Struggling with Prealgebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Given the equation $2 x + 3 y = 10$ what is the missing variable shown below?

(__, $- \frac{5}{3}$ )

$- \frac{20}{3}$

$\frac{10}{3}$

$\frac{15}{2}$

$- \frac{15}{2}$

Verified step by step guidance

Identify the given equation: $2x + 3y = 10$.

Note the given point has the form $(\_, -\frac{5}{3})$, where the $y$-coordinate is $-\frac{5}{3}$ and the $x$-coordinate is unknown.

Substitute $y = -\frac{5}{3}$ into the equation: $2x + 3\left(-\frac{5}{3}\right) = 10$.

Simplify the equation after substitution: $2x - 5 = 10$.

Solve for $x$ by isolating it: add 5 to both sides to get $2x = 15$, then divide both sides by 2 to find $x = \frac{15}{2}$.

3:07m

Watch next

Master Graphing Linear Equations in Two Variables Example 2 with a bite sized video explanation from Patrick Ford

Struggling with Prealgebra?

Given the equation 2x+3y=102x+3y=10 what is the missing variable shown below?(__, −53-\(\frac\)53)

Watch next

Given the equation $2 x + 3 y = 10$ what is the missing variable shown below?

(__, $- \frac{5}{3}$ )