Select the ordered pair from the choices below that is a solution to the following system of equations:
4y = 2x + 10
8x - 3y = -14
2x - 4y =-10
8x - 3y = -14
Multiply each side of the 1st Eq by -4
and add the 2 Eq:
-8x + 16y = 40
8x - 3y = -14
0 + 13y - 26
y = 2
Substitute 2 for y in Eq 1:
2x - 4*2 = -10
x = -1
(-1 , 2).
To find the ordered pair that is a solution to the system of equations, we can solve the system by either substitution or elimination method. Let's use the elimination method in this case.
First, let's write the system of equations in standard form:
2x - 4y = -10 (Equation 1)
8x - 3y = -14 (Equation 2)
To eliminate the x term, let's multiply Equation 1 by 4 and Equation 2 by 2:
8x - 16y = -40 (Equation 3)
16x - 6y = -28 (Equation 4)
Now, let's subtract Equation 3 from Equation 4:
(16x - 6y) - (8x - 16y) = -28 - (-40)
16x - 6y - 8x + 16y = 12
8x + 10y = 12 (Equation 5)
Next, let's solve Equations 2 and 5 simultaneously. We can multiply Equation 2 by 4 and Equation 5 by 8 to make the coefficients of x the same:
32x - 12y = -56 (Equation 6)
64x + 80y = 96 (Equation 7)
Now, subtract Equation 6 from Equation 7:
(64x + 80y) - (32x - 12y) = 96 - (-56)
64x + 80y - 32x + 12y = 152
32x + 92y = 152 (Equation 8)
Now we have a new equation with only x and y terms. Let's solve Equations 5 and 8 simultaneously.
To eliminate the x term, let's multiply Equation 8 by -4:
-128x - 368y = -608 (Equation 9)
Now, add Equation 5 and Equation 9:
(8x + 10y) + (-128x - 368y) = 12 + (-608)
8x + 10y - 128x - 368y = -596
-120x - 358y = -596
Now we have a linear equation in two variables. Let's solve it to find the value of y:
-120x - 358y = -596
-358y = -596 + 120x
y = (-596 + 120x)/(-358)
y = (298 - 60x)/179
Now, let's substitute this value of y into Equation 1 and solve for x:
2x - 4y = -10
2x - 4((298 - 60x)/179) = -10
Multiply everything by 179 to eliminate the fraction:
358x - 716(298 - 60x) = -1790
Now, simplify the equation:
358x - (214328 - 42960x) = -1790
358x - 214328 + 42960x = -1790
43318x - 214328 = -1790
43318x = -1790 + 214328
43318x = 212538
x = 212538/43318
x = 4.905
Now, substitute this value of x into Equation 1 to find y:
2x - 4y = -10
2(4.905) - 4y = -10
9.81 - 4y = -10
-4y = -10 - 9.81
-4y = -19.81
y = -19.81/-4
y = 4.9525
Therefore, the solution to the system of equations is (4.905, 4.9525).
What are your choices?
(-1, 2)
(7, 6)
(-3, 2)
(5, 5)