Solve by elimination method 5x-2y=11, 3x+4y=4.

Here, we are given with two equations. We are asked to find the value of x and y using substitution method. By using the first equation we will find the value of x by substituting the values. Then, we use the hint of x and then we can find the value of y. Then we can find the original value of x by using the value of y. Here, we also shift numbers from one hand side to the other which changes it's sign. So, let's solve!!

First let's find the value of x by using first equation.

Shift the number 2y from LHS to RHS, changing it's sign.

Shift the number 5 from LHS to RHS.

Now, let's find the value of y using the second equation.

Value of y :-

Substitute the value of x.

Multiply the number 3 with both numbers in brackets.

Convert the number 4y to like fraction and add it with the fraction.

Add the variable values on denominator.

Shift the number 5 from LHS to RHS.

Multiply the values on RHS.

Shift the number 33 from LHS to RHS, changing it's sign.

Subtract the values on RHS.

Shift the number 14 from LHS to RHS.

Now, let's find the value of x by second equation.

Value of x :-

Substitute the value of y.

Multiply the number 4 with the fraction in bracket.

Shift the fraction on LHS to RHS, changing it's sign.

Convert the values on LHS to like fractions.

Subtract those fractions now.

Shift the number 3 from LHS to RHS.

Take the reciprocal of second fraction and multiply both fractions.

Write those fractions in lowest form by cancellation method.

Write the fraction in lowest form to get the answer.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt