Answer:
4. x=2 y=3
5. x=-3, y=-6
6. x=0, y=6.5
Step-by-step explanation:
A system of equations is 2 or more equations for which the same x,y solution exists. We can solve the system in three ways: elimination, substitution, or graphing. To use substitution, we substitute a equivalent expression in for a variable and solve for the remaining variable. We then substitute again to find the other variable.
y=5x-7 & -3x-2y=-12
We will input for y, the expression 5x-7 into -3x-2y=-12. We will then isolate x to solve for it using inverse operations.
-3x-2(5x-7)=-12
-3x-10x+14=-12
-13x+14=-12
-13x+14-14=-12-14
-13x=-26
x=2
We substitute back in now to solve for y. y=5(x)-7=5(2)-7=10=7=3
-4x+y=6 & -5x-y=21
We will input for y, the expression 6+4x into -5x-y=21. We will then isolate x to solve for it using inverse operations.
-5x-(4x+6)=21
-5x-4x-6=21
-9x-6=21
-9x-6+6=21+6
-9x=27
x=-3
We substitute back in now to solve for y. y=4(x)+6=4(-3)+6=-12+6=-6
-7x-2y=-13 & x-2y=-13
We will input for x, the expression 2y-13 into -7x-2y=-13. We will then isolate y to solve for it using inverse operations.
-7(2y-13)-2y=-13
-7(2y)+-7(-13)-2y=-13
-14y+91-2y=-13
-16y+91=-13
-16y+91-91=-13-91
-16y=-104
y=6.5
We substitute back in now to solve for x. x=2y-13=2(6.5)-13=13-13=0.
