Question 618242
{{{7x^2 + y^2 = 64}}}...........(1)
{{{x + y = 4}}}.................(2)

Take (2)
{{{x + y = 4}}}
{{{x=4-y}}}.....................(3)

Put the value of x from (3) to (1)

{{{7x^2 + y^2 = 64}}}...........(1)

{{{7(4-y)^2 + y^2 = 64}}}

{{{7(16-8y+y^2) + y^2 = 64}}}

{{{112-56y+7y^2 + y^2 = 64}}}

{{{112-56y+8y^2= 64}}}

{{{8(14-7y+y^2)= 64}}}
Divide by 8 both sides of the above equation
{{{8(14-7y+y^2)/8= 64/8}}}
{{{cross(8)(14-7y+y^2)/cross(8)= cross(64)/cross(8)}}}
{{{14-7y+y^2= 8}}}
{{{14-7y+y^2-8=0}}}
{{{y^2-7y+14-8=0}}}
{{{y^2-7y+6=0}}}
Now solve for y
{{{y^2-6y-y+6=0}}}
{{{y(y-6)-1(y-6)=0}}}
{{{(y-6)(y-1)=0}}}
{{{y-6=0}}} Or {{{y-1=0}}}
{{{y=6}}} Or {{{y=1}}}

Put the values of y in (3)
{{{x=4-y}}}.....................(3)
y=6
{{{x=4-6}}}
{{{x=-2}}}
y=1
{{{x=4-1}}}
{{{x=3}}}

Solution set (x,y)=(-2,6),(3,1)





Check
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Put the values of x and y in either equation (1) or (2)

When(x,y)=(-2,6)

{{{7x^2 + y^2 = 64}}}...........(1)
{{{7(-2)^2 + (6)^2 = 64}}}
{{{7(4) + 36 = 64}}}
{{{28 + 36 = 64}}}
{{{64=64}}}

When(x,y)=(3,1)
{{{7x^2 + y^2 = 64}}}...........(1)
{{{7(3)^2 + (1)^2 = 64}}}
{{{7(9) + 1 = 64}}}
{{{63 + 1 = 64}}}
{{{64=64}}}