Mathematics, 04.02.2020 07:57 NetherisIsTheQueen

Does anyone know how to solve by substitution for 1/2x+7=y and 3y-11=-x

Answers: 3

Show answers

Answers

Substitution isn't too difficult to grasp. What you must first come to understand is that in both equations (in this particular problem) x and y are assumed to be the same numbers respectively. Meaning if you looked at the x value of the function: (Keep in mind $\frac{x}{2}$ is the same as $\frac{1}{2} x$ )
$y= \frac{x}{2} + 7$

It would be the same as the x value in the function:
-x = 3y - 11

Due to having too many variables we can't solve for a specific variable with the equations in there current form, but because they have equal values of x and y we can solve for x or y and SUBSTITUTE that value for x or y into the other equation! By doing so we eliminate a variable and make it possible to solve that equation for one of the two variables. Luckily they already solved the equations for y in the first one (Keep in mind x, and -x are not the same, thus if you want to use the -x equation you'll need to multiply all numbers by -1.

Explanation aside, let's get to the problem!
$y= \frac{x}{2} + 7$

Now we take that value for y, and substitute it in the other equation wherever there is a y.

-x = 3<img src=

- 11" alt="( \frac{x}{2}+7)" />- 11" />

Distribute the 3 to all terms in the parenthesis. (Remember only multiply the numerator by 3! (don't multiply the denominator by 3 is what I'm trying to say)... also if you have forgotten.. the numerator is the top of the fraction and the denominator is the bottom!)

$-x= \frac{3x}{2}+21 - 11$

Subtract 11 from 21.

$-x= \frac{3x}{2}+10$

Subtract 10 on both sides.

$-10-x= \frac{3x}{2}+10-10$

Simplify the right side (10-10 = 0) and add x on both sides!!

$-10 = \frac{3x}{2} +x$

Add the x's together. To do this gain a common denominator by multiplying the +x by 2/2. Then add it together!

$-10 = \frac{5x}{2}$

To get x alone we need to remove the fraction. To do that multiply by the fractions reciprocal (flip the fraction and multiply both sides by it. Keep in mind you do not want to multiply by x in this case $\frac{2}{5}*-10 = \frac{5x}{2} * \frac{2}{5}$ )

Cancel out the fraction on the right side, and multiply the -10 by 2/5. $\frac{-20}{5} = x$
x = -4

You probably are thinking... wow that's a lot of work! Well you are somewhat right, but luckily the next part is pretty easy. Pick one of the equations, and plug in the value you got for x and solve for the other variable (y). I'm going to choose the one with y already solved for.

$\frac{-4}{2} + 7 = y$
y = -2 + 7

So our answers are:
x = -4
y = 5

Answer from: Quest

for the points! : )

Answer from: Quest

by definition, an arc subtended by a central angle of some given measure has the same measure. so $(3x+18)^\circ=147^\circ$ .

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:40, helpme6191

(mc 02.03) what set of reflections and rotations would carry rectangle abcd onto itself? reflect over the y-axis, reflect over the x-axis, rotate 180° rotate 180°, reflect over the x-axis, reflect over the line y=x reflect over the x-axis, rotate 180°, reflect over the x-axis rotate 180, reflect over the y-axis, reflect over the line y=x

Answers: 1

continue

Mathematics, 22.06.2019 03:00, BardiFan

Item 1 which question could the expression 1000n answer? let n = the number of gallons of gas used. how many miles per gallon did the car get driving 1000 miles? let n = the number of grams of food needed for each dog. how many grams of food are needed to feed 1000 dogs? let n = the number of people at the show. how many empty seats were there at the show if there are 1000 seats at the theater? let n = the number of seats at the theater. how many empty seats will there by if 1000 people come to the show?

Answers: 2

continue

Mathematics, 22.06.2019 04:30, Kikilcaro9675

Dagne measures and finds that she can do a vertical jump that is 27.5% of her height. if dagne is 48 inches tall, how high can she jump? enter your answer in the box. inches

Answers: 3

continue

Mathematics, 22.06.2019 05:00, Dallas6797

Atailor in a suit shop should understand relative lengths to measurement units. which unit of measurement would normally be used to measure fabric

Answers: 3

continue

You know the right answer?

Does anyone know how to solve by substitution for 1/2x+7=y and 3y-11=-x...