[tex]\left \{ {{-3y-4x=-11} \atop {3y-5x=-61}} \right. \\-9x=-72\\x=8\\3y-5*8=-61\\3y=-21\\y=-7\\\\(8;-7)[/tex]
Answer:
x = 8
y = -7
Step-by-step explanation:
This is a system of equations called simultaneous equations.
We shall solve it by elimination method
Step 1
We shall label the equations (1) and (2)
−3y−4x=−11.....(1)
3y−5x=−61......(2)
Step 2
Multiply each term in equation (1) by 1 to give equation (3)
1(-3y-4x=-11).....(1)
-3y-4x=-11....(3)
Step 3
Multiply each term in equation 2 by -1 to give equation (4)
-1(3y−5x=−61)......(2)
-3y+5x=61.....(4)
Step 4
-3y-4x=-11....(3)
-3y+5x=61.....(4)
Subtract each term in equation (3) from each term in equation (4)
-3y-(-3y)+5x-(-4x)=61-(-11)
-3y+3y+5x+4x=61+11
0+9x=72
9x=72
Step 5
Divide both sides of the equation by 9, the coefficient of the unknown variable x to find the value of x
9x/9 = 72/9
x = 8
Step 6
Put in x = 8 into equation (2)
3y−5x=−61......(2)
3y-5(8)=-61
3y-40=-61
Collect like terms by adding 40 to both sides of the equation
3y-40+40=-61+40
3y=-21
Divide both sides by 3, the coefficient of y to find the value of y
3y/3=-21/3
y=-7
Therefore, the values of x and y that satisfy the equations are 8 and -7 respectively
