For questions 9–10, solve each system by elimination.
9. 5x + 4y = 1
3x – 4y = 7 (1 point)
(–1, –1)
(1, –1)
(1, 1)
10. x + 2y = 5
3x + y = 10 (1 point)
(3, –1)
(1, 3)
(3, 1)
9.
5x + 4y = 1
3x ? 4y = 7
what does ? mean ?
5x+4y=1
3x+4y=-7
To solve a system of equations by elimination, we eliminate one variable by adding or subtracting the equations together. Here's how to solve each of the given systems:
9.
Step 1: Multiply the second equation by 4 to eliminate the y term:
4(3x - 4y) = 4(7)
12x - 16y = 28
Step 2: Add the new equation to the first equation:
(5x + 4y) + (12x - 16y) = 1 + 28
17x - 12y = 29
Step 3: We now have a new equation in terms of x and y. Solve it to find the values of x and y:
17x - 12y = 29
There are different ways to solve this equation, but we'll use the method of substitution.
Let's solve the first equation for x in terms of y:
5x = 1 - 4y
x = (1 - 4y)/5
Now, substitute this value for x in the second equation:
17(1 - 4y)/5 - 12y = 29
Simplify the equation:
17 - 68y/5 - 12y = 29
Multiply through by 5 to get rid of the fraction:
85 - 68y - 60y = 145
Combine like terms:
-128y = 60
Divide both sides by -128:
y = -60/128
y = -15/32
Now, substitute this value for y back into the first equation to find x:
5x + 4(-15/32) = 1
5x - 60/32 = 1
5x - 15/8 = 1
5x = 1 + 15/8
5x = 8/8 + 15/8
5x = 23/8
Divide both sides by 5:
x = 23/8 * 1/5
x = 23/40
Therefore, the solution to the system is (23/40, -15/32).
The correct answer is not listed among the options given.